ArashMhasani

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0 years, 117 days

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These are questions asked by ArashMhasani

Hi
I have a huge trigonometric expression in Maple with an approximate length of length(.)=397593353.

When I compute this expression in Matlab, I receive another expression with a much smaller length, and the reason is that Matlab is using subexpressions to calculate the main expression. However, I need to do this in Maple.

I have already tried to simplify, but it didn't work.
The maple worksheet & a screenshot of the Matlab subexpression is attached.

See below file for expression in maple (Please run the "Main.mpl" in the attached file.):

Ldiff.zip

And part of the expression in Matlab is shown in the below picture

Where the subexpressions (again in Matlab) are shown below:

I want to compute the Lie derivative of a large expression in maple.
The expression is attached, there are 20 vars in total. But Maple cannot do that (after 7hrs of working!), but this is doable with another math tool which first turns the expression into subexpressions.
However, I want to do this in Maple.
I have already tried to simplify/combine/factor/use the Lie algebra package, none of them helped.
Any suggestion is highly appreciated

 

(6*m__1*(2*x[13]*x[12]*((x[12]*(cos(x[7])^2 - 2)*(x[17] - g__1)*cos(x[8])^2 - 2*x[12]*(x[17] - g__1)*cos(x[7])^2 + x[18]*cos(x[7])*sin(x[7])*sin(x[8]) + x[12]*(x[17] - g__1))*cos(x[6])^2 - 2*cos(x[8])*(x[12]*sin(x[8])*(x[17] - g__1)*sin(x[7]) + x[18]*cos(x[7])/2)*sin(x[6])*cos(x[6]) + x[12]*cos(x[8])^2*(x[17] - g__1))*cos(x[4])^5 + ((-x[12]*x[13]*x[18]*sin(x[4])*(cos(x[7])^2 - 2)*cos(x[8])^2 + (((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])*x[12]*sin(x[8])*cos(x[7])^2 - 3*(x[12]^2*x[18] - (2*x[20])/9)*sin(x[7])*cos(x[7])/2 - 2*((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])*x[12]*sin(x[8]))*cos(x[8]) + 4*(x[18]*cos(x[7])^2/2 + x[12]*sin(x[7])*sin(x[8])*(x[17] - g__1)*cos(x[7]) - x[18]/4)*sin(x[4])*x[13]*x[12])*cos(x[6])^2 + (2*((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])*sin(x[7])*x[12]*sin(x[6])*cos(x[8])^2 - 4*(x[12]*x[13]*sin(x[4])*sin(x[6])*(x[17] - g__1)*cos(x[7]) - x[13]*x[18]*sin(x[4])*sin(x[6])*sin(x[7])*sin(x[8])/2 - x[12]*x[15]*(x[17] - g__1)/24)*x[12]*cos(x[8]) - (3*(x[12]^2*x[18] - (2*x[20])/9)*sin(x[8])*cos(x[7])/2 + ((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])*sin(x[7])*x[12])*sin(x[6]))*cos(x[6]) + x[12]*(-x[13]*x[18]*cos(x[8])^2*sin(x[4]) + ((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])*sin(x[8])*cos(x[8]) + x[12]*sin(x[8])*(x[17] - g__1)*(sin(x[6])*sin(x[7])*x[15] + x[14]*cos(x[7]))/6))*cos(x[4])^4 + ((-5*x[12]^2*x[13]*(cos(x[7])^2 - 2)*(x[17] - g__1)*cos(x[8])^2 - sin(x[4])*(3*(x[12]^2*x[18] - (2*x[20])/9)*sin(x[8])*cos(x[7])^2/2 + ((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])*sin(x[7])*x[12]*cos(x[7]) - 3*(x[12]^2*x[18] - (2*x[20])/9)*sin(x[8]))*cos(x[8]) + 7*(x[12]*(x[17] - g__1)*cos(x[7])^2 - (2*x[18]*cos(x[7])*sin(x[7])*sin(x[8]))/7 - (5*x[12]*(x[17] - g__1))/7)*x[13]*x[12])*cos(x[6])^2 - (3*sin(x[4])*(x[12]^2*x[18] - (2*x[20])/9)*sin(x[7])*cos(x[8])^2 - 10*(x[18]*cos(x[7])/5 + x[12]*sin(x[8])*(x[17] - g__1)*sin(x[7]))*x[13]*x[12]*cos(x[8]) + sin(x[4])*(((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])*x[12]*sin(x[8])*cos(x[7]) - 3*(x[12]^2*x[18] - (2*x[20])/9)*sin(x[7])/2))*sin(x[6])*cos(x[6]) - 5*x[12]^2*x[13]*(x[17] - g__1)*cos(x[8])^2 - (3*sin(x[4])*(x[12]^2*x[18] - (2*x[20])/9)*sin(x[8])*cos(x[8]))/2 + (x[17] - g__1)*(x[15]*cos(x[7])*sin(x[4])*sin(x[6])/6 - x[14]*sin(x[4])*sin(x[7])/6 + x[13])*x[12]^2)*cos(x[4])^3 - (7*x[12]*((-(4*x[13]*x[18]*sin(x[4])*(cos(x[7])^2 - 2)*cos(x[8])^2)/7 + (((x[17] - g__1)*x[12]^2 + ((4*x[17])/7 - (4*g__1)/7)*x[13]^2 - (2*x[19])/7)*sin(x[8])*cos(x[7])^2 - (5*x[12]*x[18]*cos(x[7])*sin(x[7]))/7 - 2*((x[17] - g__1)*x[12]^2 + ((4*x[17])/7 - (4*g__1)/7)*x[13]^2 - (2*x[19])/7)*sin(x[8]))*cos(x[8]) + 10*(x[18]*cos(x[7])^2/5 + x[12]*sin(x[7])*sin(x[8])*(x[17] - g__1)*cos(x[7]) - (2*x[18])/5)*sin(x[4])*x[13]/7)*cos(x[6])^2 + (2*((x[17] - g__1)*x[12]^2 + ((4*x[17])/7 - (4*g__1)/7)*x[13]^2 - (2*x[19])/7)*sin(x[7])*sin(x[6])*cos(x[8])^2 + (-(10*x[12]*x[13]*sin(x[4])*sin(x[6])*(x[17] - g__1)*cos(x[7]))/7 + (8*x[13]*x[18]*sin(x[4])*sin(x[6])*sin(x[7])*sin(x[8]))/7 + x[12]*x[15]*(x[17] - g__1)/21)*cos(x[8]) - ((5*x[12]*x[18]*cos(x[7])*sin(x[8]))/7 + ((x[17] - g__1)*x[12]^2 + ((4*x[17])/7 - (4*g__1)/7)*x[13]^2 - (2*x[19])/7)*sin(x[7]))*sin(x[6]))*cos(x[6]) - (4*x[13]*x[18]*cos(x[8])^2*sin(x[4]))/7 + ((x[17] - g__1)*x[12]^2 + ((4*x[17])/7 - (4*g__1)/7)*x[13]^2 - (2*x[19])/7)*sin(x[8])*cos(x[8]) + x[12]*x[14]*sin(x[8])*(x[17] - g__1)*cos(x[7])/21 + (2*x[13]*x[18]*sin(x[4]))/7 + x[12]*x[15]*sin(x[6])*sin(x[7])*sin(x[8])*(x[17] - g__1)/21)*cos(x[4])^2)/2 + 3*(((4*x[13]*(cos(x[7])^2 - 2)*(x[17] - g__1)*cos(x[8])^2)/3 + sin(x[4])*((2*x[18]*cos(x[7])^2*sin(x[8]))/3 + x[12]*sin(x[7])*(x[17] - g__1)*cos(x[7]) - (4*x[18]*sin(x[8]))/3)*cos(x[8]) - (2*x[13]*(cos(x[7])^2 - 2)*(x[17] - g__1))/3)*cos(x[6])^2 + ((4*x[18]*cos(x[8])^2*sin(x[4])*sin(x[7]))/3 - (8*x[13]*sin(x[7])*sin(x[8])*(x[17] - g__1)*cos(x[8]))/3 + (x[12]*sin(x[8])*(x[17] - g__1)*cos(x[7]) - (2*x[18]*sin(x[7]))/3)*sin(x[4]))*sin(x[6])*cos(x[6]) + (4*x[13]*(x[17] - g__1)*cos(x[8])^2)/3 + (2*x[18]*cos(x[8])*sin(x[4])*sin(x[8]))/3 - (2*x[13]*(x[17] - g__1))/3)*x[12]^2*cos(x[4]) + 2*(x[17] - g__1)*(cos(x[8])*sin(x[8])*(cos(x[7])^2 - 2)*cos(x[6])^2 + 2*(cos(x[8])^2 - 1/2)*sin(x[7])*sin(x[6])*cos(x[6]) + cos(x[8])*sin(x[8]))*x[12]^3)*L*cos(x[5])^6 + (12*m__1*sin(x[5])*((-((x[12]^2*x[18] - x[20]/6)*(cos(x[7])^2 - 2)*cos(x[8])^2)/2 + (x[12]^2*x[18] - x[20]/6)*cos(x[7])^2 + sin(x[7])*((x[17] - g__1)*x[12]^2 + (x[17] - g__1)*x[13]^2 - x[19]/2)*x[12]*sin(x[8])*cos(x[7]) - x[12]^2*x[18]/2 + x[20]/12)*cos(x[6])^2 - (((x[17] - g__1)*x[12]^2 + (x[17] - g__1)*x[13]^2 - x[19]/2)*x[12]*cos(x[7]) - (x[12]^2*x[18] - x[20]/6)*sin(x[7])*sin(x[8]))*cos(x[8])*sin(x[6])*cos(x[6]) - cos(x[8])^2*(x[12]^2*x[18] - x[20]/6)/2)*L*cos(x[4])^5 - 6*m__1*sin(x[5])*((sin(x[4])*(cos(x[7])^2 - 2)*((x[17] - g__1)*x[12]^2 + (x[17] - g__1)*x[13]^2 - x[19]/2)*x[12]*cos(x[8])^2 + 3*x[13]*((2*x[18]*cos(x[7])^2*sin(x[8]))/3 + x[12]*sin(x[7])*(x[17] - g__1)*cos(x[7]) - (4*x[18]*sin(x[8]))/3)*x[12]*cos(x[8]) - 2*sin(x[4])*(((x[17] - g__1)*x[12]^2 + (x[17] - g__1)*x[13]^2 - x[19]/2)*x[12]*cos(x[7])^2 - (x[12]^2*x[18] - x[20]/6)*sin(x[7])*sin(x[8])*cos(x[7]) - (((x[17] - g__1)*x[12]^2 + (x[17] - g__1)*x[13]^2 - x[19]/2)*x[12])/2))*cos(x[6])^2 - 2*(-2*x[12]*x[13]*x[18]*cos(x[8])^2*sin(x[7]) + sin(x[4])*((x[12]^2*x[18] - x[20]/6)*cos(x[7]) + sin(x[7])*((x[17] - g__1)*x[12]^2 + (x[17] - g__1)*x[13]^2 - x[19]/2)*x[12]*sin(x[8]))*cos(x[8]) - 3*(x[12]*sin(x[8])*(x[17] - g__1)*cos(x[7]) - (2*x[18]*sin(x[7]))/3)*x[13]*x[12]/2)*sin(x[6])*cos(x[6]) + cos(x[8])*(sin(x[4])*((x[17] - g__1)*x[12]^2 + (x[17] - g__1)*x[13]^2 - x[19]/2)*cos(x[8]) + 2*x[13]*x[18]*sin(x[8]))*x[12])*L*cos(x[4])^4 + ((15*m__1*sin(x[5])*(cos(x[7])^2 - 2)*(x[12]^2*x[18] - (2*x[20])/15)*L*cos(x[8])^2 - 18*x[12]*((x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*sin(x[8])*cos(x[7])^2 - (2*L*x[13]*x[18]*cos(x[7])*sin(x[4])*sin(x[5])*sin(x[7])*m__1)/3 - 2*(x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*sin(x[8]))*cos(x[8]) - 33*m__1*sin(x[5])*(((7*x[12]^2*x[18])/11 - x[20]/33)*cos(x[7])^2 + ((x[17] - g__1)*x[12]^2 + ((4*x[17])/11 - (4*g__1)/11)*x[13]^2 - (2*x[19])/11)*sin(x[7])*x[12]*sin(x[8])*cos(x[7]) - (5*x[12]^2*x[18])/11 + (2*x[20])/33)*L)*cos(x[6])^2 + 33*(-12*(x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*sin(x[7])*x[12]*cos(x[8])^2/11 + m__1*sin(x[5])*(((x[17] - g__1)*x[12]^2 + ((4*x[17])/11 - (4*g__1)/11)*x[13]^2 - (2*x[19])/11)*x[12]*cos(x[7]) - 10*(x[12]^2*x[18] - (2*x[20])/15)*sin(x[7])*sin(x[8])/11)*L*cos(x[8]) + (6*x[12]*((2*L*x[13]*x[18]*cos(x[7])*sin(x[4])*sin(x[5])*sin(x[8])*m__1)/3 + (x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*sin(x[7])))/11)*sin(x[6])*cos(x[6]) + 15*m__1*sin(x[5])*(x[12]^2*x[18] - (2*x[20])/15)*L*cos(x[8])^2 - 18*(x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*x[12]*sin(x[8])*cos(x[8]) - 3*(x[12]^2*x[18] - x[20]/3)*m__1*sin(x[5])*L)*cos(x[4])^3 + 15*x[12]*((m__1*sin(x[4])*sin(x[5])*(cos(x[7])^2 - 2)*L*((x[17] - g__1)*x[12]^2 + ((4*x[17])/5 - (4*g__1)/5)*x[13]^2 - (2*x[19])/5)*cos(x[8])^2 + ((4*L*x[13]*x[18]*cos(x[7])^2*sin(x[5])*sin(x[8])*m__1)/5 + 2*(x[17] - g__1)*sin(x[7])*(L*x[12]*x[13]*sin(x[5])*m__1 - (2*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/15)*cos(x[7]) - (8*L*x[13]*x[18]*sin(x[5])*sin(x[8])*m__1)/5)*cos(x[8]) - (9*m__1*sin(x[4])*(((x[17] - g__1)*x[12]^2 + ((2*x[17])/9 - (2*g__1)/9)*x[13]^2 - x[19]/9)*cos(x[7])^2 - (5*x[12]*x[18]*cos(x[7])*sin(x[7])*sin(x[8]))/9 + (-(5*x[17])/9 + (5*g__1)/9)*x[12]^2 + (-(4*x[17])/9 + (4*g__1)/9)*x[13]^2 + (2*x[19])/9)*sin(x[5])*L)/5)*cos(x[6])^2 + ((8*L*x[13]*x[18]*cos(x[8])^2*sin(x[5])*sin(x[6])*sin(x[7])*m__1)/5 - 2*(x[12]*x[18]*cos(x[7])/2 + sin(x[7])*((x[17] - g__1)*x[12]^2 + ((4*x[17])/5 - (4*g__1)/5)*x[13]^2 - (2*x[19])/5)*sin(x[8]))*m__1*sin(x[4])*sin(x[5])*L*sin(x[6])*cos(x[8]) + 2*(x[17] - g__1)*(L*x[12]*x[13]*sin(x[5])*m__1 - (2*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/15)*sin(x[8])*sin(x[6])*cos(x[7]) - m__1*(x[12]*x[15]*sin(x[8])*(x[17] - g__1)*sin(x[4]) + 12*x[13]*x[18]*sin(x[6])*sin(x[7]))*sin(x[5])*L/15)*cos(x[6]) + m__1*sin(x[5])*(sin(x[4])*((x[17] - g__1)*x[12]^2 + ((4*x[17])/5 - (4*g__1)/5)*x[13]^2 - (2*x[19])/5)*cos(x[8])^2 + (x[12]*x[14]*sin(x[4])*(x[17] - g__1)*cos(x[7])/15 + x[12]*x[15]*sin(x[6])*sin(x[7])*(x[17] - g__1)*sin(x[4])/15 + (4*x[13]*x[18]*sin(x[8]))/5)*cos(x[8]) - sin(x[4])*((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])/5)*L)*cos(x[4])^2 + 18*x[12]*((-(2*L*x[12]*x[18]*sin(x[5])*m__1*(cos(x[7])^2 - 2)*cos(x[8])^2)/3 + 4*(x[17] - g__1)*(cos(x[7])^2 - 2)*sin(x[8])*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/6)*cos(x[8])/3 + m__1*sin(x[5])*x[12]*L*(x[18]*cos(x[7])^2/3 + x[12]*sin(x[7])*sin(x[8])*(x[17] - g__1)*cos(x[7]) - (2*x[18])/3))*cos(x[6])^2 - (-8*(x[17] - g__1)*sin(x[7])*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/6)*cos(x[8])^2/3 + m__1*sin(x[5])*(x[12]*cos(x[7])*(x[17] - g__1) - (4*x[18]*sin(x[7])*sin(x[8]))/3)*x[12]*L*cos(x[8]) + 4*(x[17] - g__1)*sin(x[7])*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/6)/3)*sin(x[6])*cos(x[6]) - (2*L*x[12]*x[18]*cos(x[8])^2*sin(x[5])*m__1)/3 + 4*(x[17] - g__1)*sin(x[8])*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/6)*cos(x[8])/3 + L*x[12]*x[18]*sin(x[5])*m__1/3)*cos(x[4]) - 12*(x[17] - g__1)*m__1*sin(x[4])*sin(x[5])*x[12]^3*L*((cos(x[8])^2 - 1/2)*(cos(x[7])^2 - 2)*cos(x[6])^2 - 2*cos(x[6])*sin(x[7])*cos(x[8])*sin(x[6])*sin(x[8]) + cos(x[8])^2 - 1/2))*cos(x[5])^5 + (-18*m__1*x[13]*L*(((cos(x[7])^2 - 2)*((x[17] - g__1)*x[12]^2 + (x[17]/3 - g__1/3)*x[13]^2 - x[19]/6)*cos(x[8])^2 + ((-2*x[17] + 2*g__1)*x[12]^2 + (-(2*x[17])/3 + (2*g__1)/3)*x[13]^2 + x[19]/3)*cos(x[7])^2 + (4*x[12]*x[18]*cos(x[7])*sin(x[7])*sin(x[8]))/3 + (x[17] - g__1)*x[12]^2 + (x[17]/3 - g__1/3)*x[13]^2 - x[19]/6)*cos(x[6])^2 - 2*((2*x[12]*x[18]*cos(x[7]))/3 + sin(x[7])*sin(x[8])*((x[17] - g__1)*x[12]^2 + (x[17]/3 - g__1/3)*x[13]^2 - x[19]/6))*cos(x[8])*sin(x[6])*cos(x[6]) + cos(x[8])^2*((x[17] - g__1)*x[12]^2 + (x[17]/3 - g__1/3)*x[13]^2 - x[19]/6))*cos(x[4])^5 + ((12*L*sin(x[4])*m__1*x[12]*x[13]*x[18]*(cos(x[7])^2 - 2)*cos(x[8])^2 - 12*m__1*L*(((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*x[12]*sin(x[8])*cos(x[7])^2 - sin(x[7])*(x[12]^2*x[18] + 5/4*x[13]^2*x[18] - 1/6*x[20])*cos(x[7]) - 2*((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*x[12]*sin(x[8]))*cos(x[8]) - 24*L*x[12]*x[13]*x[18]*cos(x[7])^2*sin(x[4])*m__1 - 36*sin(x[7])*(-x[12]*(x[17] - g__1)^2*(m__1 + m__p)*sin(x[5])/9 + m__1*sin(x[4])*x[13]*L*((x[17] - g__1)*x[12]^2 + (x[17]/3 - g__1/3)*x[13]^2 - x[19]/6))*sin(x[8])*cos(x[7]) + 12*L*sin(x[4])*m__1*x[12]*x[13]*x[18])*cos(x[6])^2 + (-24*m__1*((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*sin(x[7])*x[12]*L*sin(x[6])*cos(x[8])^2 + (36*(-x[12]*(x[17] - g__1)^2*(m__1 + m__p)*sin(x[5])/9 + m__1*sin(x[4])*x[13]*L*((x[17] - g__1)*x[12]^2 + (x[17]/3 - g__1/3)*x[13]^2 - x[19]/6))*sin(x[6])*cos(x[7]) - 24*m__1*(x[12]*x[18]*sin(x[4])*sin(x[6])*sin(x[7])*sin(x[8]) - x[13]*x[15]*(x[17] - g__1)/24)*x[13]*L)*cos(x[8]) + 12*m__1*(sin(x[8])*(x[12]^2*x[18] + 5/4*x[13]^2*x[18] - 1/6*x[20])*cos(x[7]) + ((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*sin(x[7])*x[12])*L*sin(x[6]))*cos(x[6]) - 12*m__1*(-x[12]*x[13]*x[18]*cos(x[8])^2*sin(x[4]) + ((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*x[12]*sin(x[8])*cos(x[8]) - x[13]^2*sin(x[8])*(x[17] - g__1)*(sin(x[6])*sin(x[7])*x[15] + x[14]*cos(x[7]))/12)*L)*cos(x[4])^4 + ((63*(cos(x[7])^2 - 2)*(-(2*x[12]*sin(x[4])*(x[17] - g__1)^2*(m__1 + m__p)*sin(x[5]))/63 + m__1*x[13]*L*((x[17] - g__1)*x[12]^2 + ((2*x[17])/7 - (2*g__1)/7)*x[13]^2 - (2*x[19])/21))*cos(x[8])^2 + 12*m__1*sin(x[4])*(sin(x[8])*(x[12]^2*x[18] + 5/4*x[13]^2*x[18] - 1/6*x[20])*cos(x[7])^2 + ((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*sin(x[7])*x[12]*cos(x[7]) - 2*sin(x[8])*(x[12]^2*x[18] + 5/4*x[13]^2*x[18] - 1/6*x[20]))*L*cos(x[8]) + (4*x[12]*sin(x[4])*(x[17] - g__1)^2*(m__1 + m__p)*sin(x[5]) - 63*m__1*((x[17] - g__1)*x[12]^2 - x[19]/21)*x[13]*L)*cos(x[7])^2 + 24*L*x[12]*x[13]*x[18]*cos(x[7])*sin(x[7])*sin(x[8])*m__1 - 2*x[12]*sin(x[4])*(x[17] - g__1)^2*(m__1 + m__p)*sin(x[5]) + 63*m__1*x[13]*L*((x[17] - g__1)*x[12]^2 + ((2*x[17])/7 - (2*g__1)/7)*x[13]^2 - (2*x[19])/21))*cos(x[6])^2 + 12*(2*m__1*sin(x[4])*sin(x[7])*L*(x[12]^2*x[18] + 5/4*x[13]^2*x[18] - 1/6*x[20])*cos(x[8])^2 + (-2*L*x[12]*x[13]*x[18]*cos(x[7])*m__1 - (21*sin(x[7])*(-(2*x[12]*sin(x[4])*(x[17] - g__1)^2*(m__1 + m__p)*sin(x[5]))/63 + m__1*x[13]*L*((x[17] - g__1)*x[12]^2 + ((2*x[17])/7 - (2*g__1)/7)*x[13]^2 - (2*x[19])/21))*sin(x[8]))/2)*cos(x[8]) + m__1*sin(x[4])*(((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*x[12]*sin(x[8])*cos(x[7]) - sin(x[7])*(x[12]^2*x[18] + 5/4*x[13]^2*x[18] - 1/6*x[20]))*L)*sin(x[6])*cos(x[6]) + (-2*x[12]*sin(x[4])*(x[17] - g__1)^2*(m__1 + m__p)*sin(x[5]) + 63*m__1*x[13]*L*((x[17] - g__1)*x[12]^2 + ((2*x[17])/7 - (2*g__1)/7)*x[13]^2 - (2*x[19])/21))*cos(x[8])^2 + 12*m__1*sin(x[4])*L*(x[12]^2*x[18] + 5/4*x[13]^2*x[18] - 1/6*x[20])*sin(x[8])*cos(x[8]) - 27*m__1*x[13]*(-x[13]*x[15]*sin(x[4])*sin(x[6])*(x[17] - g__1)*cos(x[7])/27 + x[13]*x[14]*sin(x[7])*(x[17] - g__1)*sin(x[4])/27 + (x[17] - g__1)*x[12]^2 + ((4*x[17])/9 - (4*g__1)/9)*x[13]^2 - x[19]/9)*L)*cos(x[4])^3 + ((-30*L*sin(x[4])*m__1*x[12]*x[13]*x[18]*(cos(x[7])^2 - 2)*cos(x[8])^2 + 24*m__1*(((x[17] - g__1)*x[12]^2 + ((17*x[17])/8 - (17*g__1)/8)*x[13]^2 - x[19]/4)*x[12]*sin(x[8])*cos(x[7])^2 - (5*sin(x[7])*x[18]*(x[12]^2 - x[13]^2/5)*cos(x[7]))/8 - 2*((x[17] - g__1)*x[12]^2 + ((17*x[17])/8 - (17*g__1)/8)*x[13]^2 - x[19]/4)*x[12]*sin(x[8]))*L*cos(x[8]) + 12*L*x[12]*x[13]*x[18]*cos(x[7])^2*sin(x[4])*m__1 + 45*(x[17] - g__1)*sin(x[7])*(-(4*x[12]*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/45 + L*x[13]*sin(x[4])*m__1*(x[12]^2 - (2*x[13]^2)/15))*sin(x[8])*cos(x[7]) - 30*L*sin(x[4])*m__1*x[12]*x[13]*x[18])*cos(x[6])^2 + (48*m__1*sin(x[7])*((x[17] - g__1)*x[12]^2 + ((17*x[17])/8 - (17*g__1)/8)*x[13]^2 - x[19]/4)*x[12]*L*sin(x[6])*cos(x[8])^2 + (-45*(x[17] - g__1)*(-(4*x[12]*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/45 + L*x[13]*sin(x[4])*m__1*(x[12]^2 - (2*x[13]^2)/15))*sin(x[6])*cos(x[7]) + m__1*(60*x[12]*x[13]*x[18]*sin(x[4])*sin(x[6])*sin(x[7])*sin(x[8]) + x[15]*(x[12] - x[13])*(x[12] + x[13])*(x[17] - g__1))*L)*cos(x[8]) - 24*m__1*((5*x[18]*sin(x[8])*(x[12]^2 - x[13]^2/5)*cos(x[7]))/8 + sin(x[7])*((x[17] - g__1)*x[12]^2 + ((17*x[17])/8 - (17*g__1)/8)*x[13]^2 - x[19]/4)*x[12])*L*sin(x[6]))*cos(x[6]) + 24*m__1*(-(5*x[12]*x[13]*x[18]*cos(x[8])^2*sin(x[4]))/4 + ((x[17] - g__1)*x[12]^2 + ((17*x[17])/8 - (17*g__1)/8)*x[13]^2 - x[19]/4)*x[12]*sin(x[8])*cos(x[8]) + x[14]*sin(x[8])*(x[12] - x[13])*(x[12] + x[13])*(x[17] - g__1)*cos(x[7])/24 + (3*x[12]*x[13]*x[18]*sin(x[4]))/4 + x[15]*sin(x[6])*sin(x[7])*sin(x[8])*(x[12] - x[13])*(x[12] + x[13])*(x[17] - g__1)/24)*L)*cos(x[4])^2 - 18*x[12]*((8*(x[17] - g__1)*(cos(x[7])^2 - 2)*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/12 + L*x[12]*x[13]*m__1)*cos(x[8])^2/3 + m__1*sin(x[4])*((2*x[12]*x[18]*cos(x[7])^2*sin(x[8]))/3 + (x[17] - g__1)*(x[12]^2 - x[13]^2/3)*sin(x[7])*cos(x[7]) - (4*x[12]*x[18]*sin(x[8]))/3)*L*cos(x[8]) - (x[17] - g__1)*((-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/9 + L*x[12]*x[13]*m__1)*cos(x[7])^2 + (2*sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/9 - (8*L*x[12]*x[13]*m__1)/3))*cos(x[6])^2 + ((4*L*x[12]*x[18]*cos(x[8])^2*sin(x[4])*sin(x[7])*m__1)/3 - 16*(x[17] - g__1)*sin(x[7])*sin(x[8])*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/12 + L*x[12]*x[13]*m__1)*cos(x[8])/3 + m__1*sin(x[4])*((x[17] - g__1)*(x[12]^2 - x[13]^2/3)*sin(x[8])*cos(x[7]) - (2*x[12]*x[18]*sin(x[7]))/3)*L)*sin(x[6])*cos(x[6]) + 8*(x[17] - g__1)*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/12 + L*x[12]*x[13]*m__1)*cos(x[8])^2/3 + (2*L*x[12]*x[18]*cos(x[8])*sin(x[4])*sin(x[8])*m__1)/3 - 5*(x[17] - g__1)*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/15 + L*x[12]*x[13]*m__1)/3)*cos(x[4]) - 12*(x[17] - g__1)*m__1*(cos(x[8])*sin(x[8])*(cos(x[7])^2 - 2)*cos(x[6])^2 + 2*(cos(x[8])^2 - 1/2)*sin(x[7])*sin(x[6])*cos(x[6]) + cos(x[8])*sin(x[8]))*x[12]^3*L)*cos(x[5])^4 + (-36*m__1*sin(x[5])*x[13]^2*((-x[18]*(cos(x[7])^2 - 2)*cos(x[8])^2/6 + x[18]*cos(x[7])^2/3 + x[12]*sin(x[7])*sin(x[8])*(x[17] - g__1)*cos(x[7]) - x[18]/6)*cos(x[6])^2 - cos(x[8])*(x[12]*cos(x[7])*(x[17] - g__1) - x[18]*sin(x[7])*sin(x[8])/3)*sin(x[6])*cos(x[6]) - x[18]*cos(x[8])^2/6)*L*cos(x[4])^5 + 36*((((x[17] - g__1)*(cos(x[7])^2 - 2)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/9)*cos(x[8])^2)/2 + m__1*sin(x[5])*((2*x[12]*x[18]*cos(x[7])^2*sin(x[8]))/3 + sin(x[7])*((x[17] - g__1)*x[12]^2 + (x[17]/2 - g__1/2)*x[13]^2 - x[19]/6)*cos(x[7]) - (4*x[12]*x[18]*sin(x[8]))/3)*L*cos(x[8]) - (x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/9)*cos(x[7])^2 + L*x[13]*x[18]*cos(x[7])*sin(x[4])*sin(x[5])*sin(x[7])*sin(x[8])*m__1/3 + ((x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/9))/2)*cos(x[6])^2 + ((4*L*x[12]*x[18]*cos(x[8])^2*sin(x[5])*sin(x[7])*m__1)/3 + (-L*x[13]*x[18]*cos(x[7])*sin(x[4])*sin(x[5])*m__1/3 - (x[17] - g__1)*sin(x[7])*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/9)*sin(x[8]))*cos(x[8]) + m__1*sin(x[5])*L*(sin(x[8])*((x[17] - g__1)*x[12]^2 + (x[17]/2 - g__1/2)*x[13]^2 - x[19]/6)*cos(x[7]) - (2*x[12]*x[18]*sin(x[7]))/3))*sin(x[6])*cos(x[6]) + cos(x[8])*((x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/9)*cos(x[8]) + (4*L*x[12]*x[18]*sin(x[5])*sin(x[8])*m__1)/3)/2)*x[13]*cos(x[4])^4 + ((-6*m__1*sin(x[5])*(cos(x[7])^2 - 2)*L*(x[12]^2*x[18] + 5/2*x[13]^2*x[18] - 1/6*x[20])*cos(x[8])^2 + (36*(m__1*sin(x[4])*x[13]*L*((x[17] - g__1)*x[12]^2 + (x[17]/2 - g__1/2)*x[13]^2 - x[19]/6)*sin(x[5]) - (11*x[12]*(x[17] - g__1)^2*(m__1 + m__p))/36)*sin(x[8])*cos(x[7])^2 - 24*sin(x[7])*x[18]*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/6)*cos(x[7]) - 72*(m__1*sin(x[4])*x[13]*L*((x[17] - g__1)*x[12]^2 + (x[17]/2 - g__1/2)*x[13]^2 - x[19]/6)*sin(x[5]) - (11*x[12]*(x[17] - g__1)^2*(m__1 + m__p))/36)*sin(x[8]))*cos(x[8]) + 3*L*x[13]^2*x[18]*cos(x[7])^2*sin(x[5])*m__1 + 27*(x[17] - g__1)*x[13]*sin(x[7])*(L*x[12]*x[13]*sin(x[5])*m__1 - (4*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/27)*sin(x[8])*cos(x[7]) - 6*m__1*sin(x[5])*L*(x[12]^2*x[18] + 5/2*x[13]^2*x[18] - 1/6*x[20]))*cos(x[6])^2 + (72*(m__1*sin(x[4])*x[13]*L*((x[17] - g__1)*x[12]^2 + (x[17]/2 - g__1/2)*x[13]^2 - x[19]/6)*sin(x[5]) - (11*x[12]*(x[17] - g__1)^2*(m__1 + m__p))/36)*sin(x[7])*sin(x[6])*cos(x[8])^2 + (-27*(x[17] - g__1)*x[13]*(L*x[12]*x[13]*sin(x[5])*m__1 - (4*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/27)*sin(x[6])*cos(x[7]) + 12*m__1*sin(x[7])*L*(x[12]^2*x[18] + 5/2*x[13]^2*x[18] - 1/6*x[20])*sin(x[8])*sin(x[6])*sin(x[5]) + x[15]*(x[17] - g__1)^2*(m__1 + m__p))*cos(x[8]) - 36*((2*x[18]*sin(x[8])*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/6)*cos(x[7]))/3 + (m__1*sin(x[4])*x[13]*L*((x[17] - g__1)*x[12]^2 + (x[17]/2 - g__1/2)*x[13]^2 - x[19]/6)*sin(x[5]) - (11*x[12]*(x[17] - g__1)^2*(m__1 + m__p))/36)*sin(x[7]))*sin(x[6]))*cos(x[6]) - 6*m__1*sin(x[5])*L*(x[12]^2*x[18] + 5/2*x[13]^2*x[18] - 1/6*x[20])*cos(x[8])^2 + 36*(m__1*sin(x[4])*x[13]*L*((x[17] - g__1)*x[12]^2 + (x[17]/2 - g__1/2)*x[13]^2 - x[19]/6)*sin(x[5]) - (11*x[12]*(x[17] - g__1)^2*(m__1 + m__p))/36)*sin(x[8])*cos(x[8]) + x[14]*sin(x[8])*(x[17] - g__1)^2*(m__1 + m__p)*cos(x[7]) + 6*m__1*(x[12]^2*x[18] + 3/2*x[13]^2*x[18] - 1/6*x[20])*L*sin(x[5]) + x[15]*sin(x[6])*sin(x[7])*sin(x[8])*(x[17] - g__1)^2*(m__1 + m__p))*cos(x[4])^3 + ((-6*(cos(x[7])^2 - 2)*(m__1*sin(x[4])*x[12]*((x[17] - g__1)*x[12]^2 + ((15*x[17])/2 - (15*g__1)/2)*x[13]^2 - x[19]/2)*L*sin(x[5]) - (11*x[13]*(x[17] - g__1)^2*(m__1 + m__p))/6)*cos(x[8])^2 + (-24*(L*x[12]*x[13]*sin(x[5])*m__1 - sin(x[4])*(m__1 + m__p)*(x[17] - g__1)/6)*x[18]*sin(x[8])*cos(x[7])^2 - 42*(x[17] - g__1)*(L*x[13]*m__1*(x[12]^2 - x[13]^2/7)*sin(x[5]) - (11*x[12]*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/42)*sin(x[7])*cos(x[7]) + 48*(L*x[12]*x[13]*sin(x[5])*m__1 - sin(x[4])*(m__1 + m__p)*(x[17] - g__1)/6)*x[18]*sin(x[8]))*cos(x[8]) + 9*(x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 + 5*(m__1 + m__p)*(x[17] - g__1)/9)*x[13]*cos(x[7])^2 + 3*L*x[13]^2*x[18]*cos(x[7])*sin(x[4])*sin(x[5])*sin(x[7])*sin(x[8])*m__1 - 6*m__1*sin(x[4])*x[12]*((x[17] - g__1)*x[12]^2 + ((15*x[17])/2 - (15*g__1)/2)*x[13]^2 - x[19]/2)*L*sin(x[5]) + 11*x[13]*(x[17] - g__1)^2*(m__1 + m__p))*cos(x[6])^2 + (-48*(L*x[12]*x[13]*sin(x[5])*m__1 - sin(x[4])*(m__1 + m__p)*(x[17] - g__1)/6)*sin(x[7])*x[18]*sin(x[6])*cos(x[8])^2 + 12*(-L*x[13]^2*x[18]*cos(x[7])*sin(x[4])*sin(x[5])*m__1/4 + sin(x[7])*(m__1*sin(x[4])*x[12]*((x[17] - g__1)*x[12]^2 + ((15*x[17])/2 - (15*g__1)/2)*x[13]^2 - x[19]/2)*L*sin(x[5]) - (11*x[13]*(x[17] - g__1)^2*(m__1 + m__p))/6)*sin(x[8]))*sin(x[6])*cos(x[8]) - 42*(x[17] - g__1)*(L*x[13]*m__1*(x[12]^2 - x[13]^2/7)*sin(x[5]) - (11*x[12]*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/42)*sin(x[8])*sin(x[6])*cos(x[7]) + 24*m__1*(-x[13]*x[15]*sin(x[8])*(x[17] - g__1)*sin(x[4])/24 + x[12]*x[18]*sin(x[6])*sin(x[7]))*x[13]*L*sin(x[5]) - 4*x[18]*sin(x[4])*sin(x[6])*sin(x[7])*(m__1 + m__p)*(x[17] - g__1))*cos(x[6]) + (-6*m__1*sin(x[4])*x[12]*((x[17] - g__1)*x[12]^2 + ((15*x[17])/2 - (15*g__1)/2)*x[13]^2 - x[19]/2)*L*sin(x[5]) + 11*x[13]*(x[17] - g__1)^2*(m__1 + m__p))*cos(x[8])^2 + (L*x[13]^2*x[14]*sin(x[4])*sin(x[5])*m__1*(x[17] - g__1)*cos(x[7]) - 24*m__1*(-x[13]*x[15]*sin(x[6])*sin(x[7])*(x[17] - g__1)*sin(x[4])/24 + x[12]*x[18]*sin(x[8]))*x[13]*L*sin(x[5]) + 4*x[18]*sin(x[4])*sin(x[8])*(m__1 + m__p)*(x[17] - g__1))*cos(x[8]) + x[15]*sin(x[4])*sin(x[6])*(x[17] - g__1)^2*(m__1 + m__p)*cos(x[7]) + 6*m__1*sin(x[4])*((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*x[12]*L*sin(x[5]) - 9*(x[17] - g__1)^2*(x[14]*sin(x[4])*sin(x[7])/9 + x[13])*(m__1 + m__p))*cos(x[4])^2 + ((6*L*sin(x[5])*m__1*x[12]^2*x[18]*(cos(x[7])^2 - 2)*cos(x[8])^2 - 36*(x[17] - g__1)*((L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*x[12]*sin(x[8])*cos(x[7])^2 - x[18]*sin(x[7])*(m__1 + m__p)*cos(x[7])/9 - 2*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*x[12]*sin(x[8]))*cos(x[8]) + 6*(x[17] - g__1)*x[13]*sin(x[7])*(L*x[12]*x[13]*sin(x[5])*m__1 - (7*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/6)*sin(x[8])*cos(x[7]) + 6*L*sin(x[5])*m__1*x[12]^2*x[18])*cos(x[6])^2 + (-72*(x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*sin(x[7])*x[12]*sin(x[6])*cos(x[8])^2 + (-6*(x[17] - g__1)*x[13]*(L*x[12]*x[13]*sin(x[5])*m__1 - (7*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/6)*sin(x[6])*cos(x[7]) - 12*L*x[12]^2*x[18]*sin(x[5])*sin(x[6])*sin(x[7])*sin(x[8])*m__1 - x[15]*(x[17] - g__1)^2*(m__1 + m__p))*cos(x[8]) + 36*(x[17] - g__1)*(x[18]*sin(x[8])*(m__1 + m__p)*cos(x[7])/9 + (L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*sin(x[7])*x[12])*sin(x[6]))*cos(x[6]) + 6*L*sin(x[5])*cos(x[8])^2*m__1*x[12]^2*x[18] - 36*(x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*x[12]*sin(x[8])*cos(x[8]) - x[14]*sin(x[8])*(x[17] - g__1)^2*(m__1 + m__p)*cos(x[7]) - 6*L*sin(x[5])*m__1*x[12]^2*x[18] - x[15]*sin(x[6])*sin(x[7])*sin(x[8])*(x[17] - g__1)^2*(m__1 + m__p))*cos(x[4]) + 6*(x[17] - g__1)*sin(x[4])*x[12]*((L*x[12]^2*sin(x[5])*m__1*(cos(x[7])^2 - 2)*cos(x[8])^2 + (7*cos(x[7])*sin(x[7])*(m__1 + m__p)*(x[17] - g__1)*cos(x[8]))/6 + L*x[12]^2*sin(x[5])*m__1)*cos(x[6])^2 - 2*(L*x[12]^2*cos(x[8])*sin(x[5])*sin(x[7])*m__1 - (7*cos(x[7])*(m__1 + m__p)*(x[17] - g__1))/12)*sin(x[8])*sin(x[6])*cos(x[6]) + L*x[12]^2*sin(x[5])*m__1*(cos(x[8]) - 1)*(cos(x[8]) + 1)))*cos(x[5])^3 + (6*(((cos(x[7])^2 - 2)*cos(x[8])^2 - 2*cos(x[7])^2 + 1)*cos(x[6])^2 - 2*cos(x[6])*sin(x[7])*cos(x[8])*sin(x[6])*sin(x[8]) + cos(x[8])^2)*(x[17] - g__1)*m__1*x[13]^3*L*cos(x[4])^5 + 36*m__1*x[13]^2*(((x[12]*sin(x[8])*(x[17] - g__1)*cos(x[7])^2 - x[18]*cos(x[7])*sin(x[7])/3 - 2*x[12]*sin(x[8])*(x[17] - g__1))*cos(x[8]) + x[13]*cos(x[7])*sin(x[4])*sin(x[7])*sin(x[8])*(x[17] - g__1)/3)*cos(x[6])^2 + 2*(x[12]*sin(x[7])*(x[17] - g__1)*cos(x[8])^2 - x[13]*sin(x[4])*cos(x[7])*(x[17] - g__1)*cos(x[8])/6 - x[18]*cos(x[7])*sin(x[8])/6 - x[12]*sin(x[7])*(x[17] - g__1)/2)*sin(x[6])*cos(x[6]) + x[12]*cos(x[8])*sin(x[8])*(x[17] - g__1))*L*cos(x[4])^4 - 18*x[13]*((m__1*((x[17] - g__1)*x[12]^2 + ((7*x[17])/6 - (7*g__1)/6)*x[13]^2 - x[19]/6)*(cos(x[7])^2 - 2)*L*cos(x[8])^2 + ((2*L*x[13]*x[18]*cos(x[7])^2*sin(x[4])*sin(x[8])*m__1)/3 + 2*(x[17] - g__1)*(-11*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/36 + L*x[12]*x[13]*sin(x[4])*m__1)*sin(x[7])*cos(x[7]) - (4*L*x[13]*x[18]*sin(x[4])*sin(x[8])*m__1)/3)*cos(x[8]) + m__1*(((x[17] - g__1)*x[13]^2*cos(x[7])^2)/6 + (x[17] - g__1)*x[12]^2 + ((7*x[17])/6 - (7*g__1)/6)*x[13]^2 - x[19]/6)*L)*cos(x[6])^2 - 2*(-(2*L*x[13]*x[18]*cos(x[8])^2*sin(x[4])*sin(x[7])*m__1)/3 + m__1*((x[17] - g__1)*x[12]^2 + ((7*x[17])/6 - (7*g__1)/6)*x[13]^2 - x[19]/6)*sin(x[7])*L*sin(x[8])*cos(x[8]) - (x[17] - g__1)*(-11*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/36 + L*x[12]*x[13]*sin(x[4])*m__1)*sin(x[8])*cos(x[7]) + L*x[13]*x[18]*sin(x[4])*sin(x[7])*m__1/3)*sin(x[6])*cos(x[6]) + (((x[17] - g__1)*x[12]^2 + ((7*x[17])/6 - (7*g__1)/6)*x[13]^2 - x[19]/6)*cos(x[8])^2 + (2*x[13]*x[18]*cos(x[8])*sin(x[4])*sin(x[8]))/3 + (g__1 - x[17])*x[12]^2 + (-(5*x[17])/6 + (5*g__1)/6)*x[13]^2 + x[19]/6)*m__1*L)*cos(x[4])^3 + ((12*(-((m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/3 + L*x[12]*x[13]*sin(x[4])*m__1)*(cos(x[7])^2 - 2)*x[18]*cos(x[8])^2 - 36*x[13]*((x[17] - g__1)*sin(x[8])*(-(11*sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/36 + L*x[12]*x[13]*m__1)*cos(x[7])^2 + L*x[13]*x[18]*cos(x[7])*sin(x[7])*m__1/12 - 2*(x[17] - g__1)*sin(x[8])*(-(11*sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/36 + L*x[12]*x[13]*m__1))*cos(x[8]) - 4*x[18]*sin(x[5])*(m__1 + m__p)*(x[17] - g__1)*cos(x[7])^2 + 9*(x[17] - g__1)*(-(10*x[12]*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/9 + L*x[13]^3*sin(x[4])*m__1)*sin(x[7])*sin(x[8])*cos(x[7]) + 12*(-((m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/3 + L*x[12]*x[13]*sin(x[4])*m__1)*x[18])*cos(x[6])^2 + (-72*(x[17] - g__1)*x[13]*sin(x[7])*(-(11*sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/36 + L*x[12]*x[13]*m__1)*sin(x[6])*cos(x[8])^2 + (-9*(x[17] - g__1)*(-(10*x[12]*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/9 + L*x[13]^3*sin(x[4])*m__1)*sin(x[6])*cos(x[7]) + 8*x[18]*sin(x[6])*sin(x[7])*sin(x[8])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]) - 24*m__1*(x[12]*x[18]*sin(x[4])*sin(x[6])*sin(x[7])*sin(x[8]) - x[13]*x[15]*(x[17] - g__1)/24)*x[13]*L)*cos(x[8]) + 36*(-L*x[13]*x[18]*cos(x[7])*sin(x[8])*m__1/12 + (x[17] - g__1)*sin(x[7])*(-(11*sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/36 + L*x[12]*x[13]*m__1))*x[13]*sin(x[6]))*cos(x[6]) + 12*(-((m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/3 + L*x[12]*x[13]*sin(x[4])*m__1)*x[18]*cos(x[8])^2 - 36*(x[17] - g__1)*x[13]*sin(x[8])*(-(11*sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/36 + L*x[12]*x[13]*m__1)*cos(x[8]) + L*x[13]^2*x[14]*sin(x[8])*m__1*(x[17] - g__1)*cos(x[7]) + 4*x[18]*sin(x[5])*(m__1 + m__p)*(x[17] - g__1) - 12*m__1*x[13]*L*(x[12]*x[18]*sin(x[4]) - x[13]*x[15]*sin(x[6])*sin(x[7])*sin(x[8])*(x[17] - g__1)/12))*cos(x[4])^2 + 18*(x[17] - g__1)*(((cos(x[7])^2 - 2)*x[12]*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/3 + L*x[12]*x[13]*m__1)*cos(x[8])^2 - ((-7*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/6 + L*x[12]*x[13]*sin(x[4])*m__1)*x[13]*sin(x[7])*cos(x[7])*cos(x[8]))/3 - (5*x[12]*sin(x[4])*sin(x[5])*(m__1 + m__p)*(x[17] - g__1)*cos(x[7])^2)/9 + (2*x[18]*sin(x[4])*sin(x[5])*sin(x[7])*sin(x[8])*(m__1 + m__p)*cos(x[7]))/9 + x[12]*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/3 + L*x[12]*x[13]*m__1))*cos(x[6])^2 + (-2*(x[18]*sin(x[4])*sin(x[5])*(m__1 + m__p)*cos(x[7])/9 + sin(x[7])*x[12]*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/3 + L*x[12]*x[13]*m__1)*sin(x[8]))*sin(x[6])*cos(x[8]) - (((-7*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/6 + L*x[12]*x[13]*sin(x[4])*m__1)*x[13]*sin(x[6])*cos(x[7]) + x[15]*sin(x[4])*sin(x[5])*(m__1 + m__p)*(x[17] - g__1)/6)*sin(x[8]))/3)*cos(x[6]) + x[12]*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/3 + L*x[12]*x[13]*m__1)*cos(x[8])^2 + sin(x[4])*sin(x[5])*(m__1 + m__p)*(x[17] - g__1)*(sin(x[6])*sin(x[7])*x[15] + x[14]*cos(x[7]))*cos(x[8])/18 - x[12]*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/3 + L*x[12]*x[13]*m__1))*cos(x[4]) + 7*x[12]*cos(x[6])*cos(x[7])*sin(x[5])*(x[17] - g__1)^2*(m__1 + m__p)*(cos(x[6])*sin(x[7])*sin(x[8]) - sin(x[6])*cos(x[8])))*cos(x[5])^2 + (-12*L*x[13]^3*cos(x[6])*cos(x[7])*sin(x[5])*m__1*(cos(x[6])*sin(x[7])*cos(x[8]) + sin(x[6])*sin(x[8]))*(x[17] - g__1)*cos(x[4])^4 - 12*m__1*sin(x[5])*x[13]^2*(((-x[18]*cos(x[7])^2/2 + x[18])*cos(x[8])^2 + x[13]*sin(x[4])*sin(x[8])*(cos(x[7])^2 - 2)*(x[17] - g__1)*cos(x[8]) - x[18]/2)*cos(x[6])^2 + 2*(x[13]*sin(x[4])*(x[17] - g__1)*cos(x[8])^2 + x[18]*cos(x[8])*sin(x[8])/2 - x[13]*sin(x[4])*(x[17] - g__1)/2)*sin(x[7])*sin(x[6])*cos(x[6]) - x[18]*cos(x[8])^2/2 + x[13]*sin(x[4])*sin(x[8])*(x[17] - g__1)*cos(x[8]) + x[18]/2)*L*cos(x[4])^3 + 18*(x[17] - g__1)*x[13]*(((L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/3)*(cos(x[7])^2 - 2)*cos(x[8])^2 - L*x[13]^2*cos(x[7])*cos(x[8])*sin(x[5])*sin(x[7])*m__1/3 - 5*(m__1 + m__p)*(x[17] - g__1)*cos(x[7])^2/9 + L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/3)*cos(x[6])^2 - 2*sin(x[8])*((L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/3)*sin(x[7])*cos(x[8]) + L*x[13]^2*cos(x[7])*sin(x[5])*m__1/6)*sin(x[6])*cos(x[6]) + (cos(x[8]) + 1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/3)*(cos(x[8]) - 1))*cos(x[4])^2 + 10*(x[17] - g__1)*(sin(x[7])*cos(x[7])*(-(2*x[18]*cos(x[8]))/5 + x[13]*sin(x[4])*sin(x[8])*(x[17] - g__1))*cos(x[6])^2 + (-(x[17] - g__1)*(x[13]*cos(x[7])*sin(x[4])*sin(x[6]) - x[15]/10)*cos(x[8]) - (2*x[18]*cos(x[7])*sin(x[6])*sin(x[8]))/5)*cos(x[6]) + sin(x[8])*(x[17] - g__1)*(sin(x[6])*sin(x[7])*x[15] + x[14]*cos(x[7]))/10)*(m__1 + m__p)*cos(x[4]) - 7*x[12]*cos(x[6])*cos(x[7])*sin(x[4])*(x[17] - g__1)^2*(m__1 + m__p)*(cos(x[6])*sin(x[7])*cos(x[8]) + sin(x[6])*sin(x[8])))*cos(x[5]) + 6*(x[17] - g__1)*cos(x[4])*x[13]*(((1 + (cos(x[7])^2 - 2)*cos(x[8])^2)*cos(x[6])^2 - 2*cos(x[6])*sin(x[7])*cos(x[8])*sin(x[6])*sin(x[8]) + cos(x[8])^2 - 1)*m__1*x[13]^2*L*cos(x[4])^2 - (7*cos(x[6])*cos(x[7])*sin(x[5])*(m__1 + m__p)*(cos(x[6])*sin(x[7])*cos(x[8]) + sin(x[6])*sin(x[8]))*(x[17] - g__1))/6))/(cos(x[4])^4*m__1*(((((cos(x[7])^2 - 2)*cos(x[8])^2 - 2*cos(x[7])^2 + 1)*cos(x[6])^2 - 2*cos(x[6])*sin(x[7])*cos(x[8])*sin(x[6])*sin(x[8]) + cos(x[8])^2)*cos(x[4])^2 + 2*cos(x[6])*cos(x[7])*sin(x[4])*(cos(x[6])*sin(x[7])*sin(x[8]) - sin(x[6])*cos(x[8]))*cos(x[4]) - 2*(cos(x[8])^2 - 1/2)*(cos(x[7])^2 - 2)*cos(x[6])^2 + 4*cos(x[6])*sin(x[7])*cos(x[8])*sin(x[6])*sin(x[8]) - 2*cos(x[8])^2 + 1)*cos(x[5])^2 - 2*sin(x[5])*(cos(x[6])*cos(x[7])*(cos(x[6])*sin(x[7])*cos(x[8]) + sin(x[6])*sin(x[8]))*cos(x[4]) + sin(x[4])*(cos(x[8])*sin(x[8])*(cos(x[7])^2 - 2)*cos(x[6])^2 + 2*(cos(x[8])^2 - 1/2)*sin(x[7])*sin(x[6])*cos(x[6]) + cos(x[8])*sin(x[8])))*cos(x[5]) + (1 + (cos(x[7])^2 - 2)*cos(x[8])^2)*cos(x[6])^2 - 2*cos(x[6])*sin(x[7])*cos(x[8])*sin(x[6])*sin(x[8]) + cos(x[8])^2 - 1)*L*cos(x[5])^4)

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