Christopher2222

MaplePrimes Activity


These are answers submitted by Christopher2222

Sorry to bring this old post up (a search led me to this post).  However this actually was possible back in 2006.  In 2006 that would be Maple 10 at the time.  Kitonums solution here https://www.mapleprimes.com/questions/200601-Labels-Above-Axis#answer202152
actually works without the align command option. 

I removed a lot of the outputs in the file, they seemed to filled with hyperlink errors or something.  Anyway don't know if it helps but you can load the sheet into Maple now.

triangle_analysis2.mw

The operator may have mistyped something.  I have given him a free pass and typed it out.  Not responsible for any errors I may have made, but I have fixed it and reuploaded it 3 times already for various errors (I'm done with that).


 

restart

with(Physics)

Setup(mathematicalnotation = true)

Eq1 := m1*l1^2*(diff(theta1(t), t, t))+(1/2)*m2*(2*l1^2*(diff(theta1(t), t, t))+2*l1*l2*(diff(theta2(t), t, t))*(sin(theta1(t))*sin(theta2(t))+cos(theta1(t))*cos(theta2(t)))+2*l1*l2*(diff(theta2(t), t))*((diff(theta1(t), t))*cos(theta1(t))*sin(theta2(t))+sin(theta1(t))*(diff(theta2(t), t))*cos(theta2(t))-(diff(theta1(t), t))*sin(theta1(t))*cos(theta2(t))-cos(theta1(t))*(diff(theta2(t), t))*sin(theta2(t)))) = thaw1-thaw2

m1*l1^2*(diff(diff(theta1(t), t), t))+(1/2)*m2*(2*l1^2*(diff(diff(theta1(t), t), t))+2*l1*l2*(diff(diff(theta2(t), t), t))*(sin(theta1(t))*sin(theta2(t))+cos(theta1(t))*cos(theta2(t)))+2*l1*l2*(diff(theta2(t), t))*((diff(theta1(t), t))*cos(theta1(t))*sin(theta2(t))+sin(theta1(t))*(diff(theta2(t), t))*cos(theta2(t))-(diff(theta1(t), t))*sin(theta1(t))*cos(theta2(t))-cos(theta1(t))*(diff(theta2(t), t))*sin(theta2(t)))) = thaw1-thaw2

(1)

Eq2 := (1/2)*m2*(2*l2^2*(diff(theta2(t), t, t))+2*l1*l2*(diff(theta1(t), t, t))*(sin(theta1(t))*sin(theta2(t))+cos(theta1(t))*cos(theta2(t))+2*l1*l2*(diff(theta1(t), t))*((diff(theta1(t), t))*cos(theta1(t))*sin(theta2(t))+sin(theta1(t))*(diff(theta2(t), t))*cos(theta2(t))-(diff(theta1(t), t))*sin(theta1(t))*cos(theta2(t))-cos(theta1(t))*(diff(theta2(t), t))*sin(t)))) = thaw2

(1/2)*m2*(2*l2^2*(diff(diff(theta2(t), t), t))+2*l1*l2*(diff(diff(theta1(t), t), t))*(sin(theta1(t))*sin(theta2(t))+cos(theta1(t))*cos(theta2(t))+2*l1*l2*(diff(theta1(t), t))*((diff(theta1(t), t))*cos(theta1(t))*sin(theta2(t))+sin(theta1(t))*(diff(theta2(t), t))*cos(theta2(t))-(diff(theta1(t), t))*sin(theta1(t))*cos(theta2(t))-cos(theta1(t))*(diff(theta2(t), t))*sin(t)))) = thaw2

(2)

``

(1/2)*m2*(2*l2^2*(diff(diff(theta2(t), t), t))+2*l1*l2*(diff(diff(theta1(t), t), t))*(sin(theta1)*sin(theta2)+cos(theta1)*cos(theta2))+2*l1*l2*(diff(theta1(t), t))*((diff(theta1(t), t))*cos(theta1)*sin(theta2)+sin(theta1)*(diff(theta2(t), t))*cos(theta2)-(diff(theta1(t), t))*sin(theta1)*cos(theta2)-cos(theta1)*(diff(theta2(t), t))*sin(theta2)))

(3)

solve([Eq1, Eq2], {diff(theta1(t), t, t), diff(theta2(t), t, t)})

{diff(diff(theta1(t), t), t) = (-sin(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2+sin(theta1(t))*cos(theta2(t))*(diff(theta2(t), t))^2*l1*l2^2*m2+sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2-sin(theta2(t))*cos(theta1(t))*(diff(theta2(t), t))^2*l1*l2^2*m2+sin(theta1(t))*sin(theta2(t))*l1*thaw2+cos(theta1(t))*cos(theta2(t))*l1*thaw2-thaw1*l2+thaw2*l2)/(l1^2*(-2*sin(theta1(t))^2*sin(theta2(t))*cos(theta2(t))*(diff(theta1(t), t))^2*l1*l2*m2+2*sin(theta1(t))^2*sin(theta2(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2*m2+2*sin(theta1(t))*sin(theta2(t))^2*cos(theta1(t))*(diff(theta1(t), t))^2*l1*l2*m2-2*sin(theta1(t))*sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*sin(t)*l1*l2*m2-2*sin(theta1(t))*cos(theta1(t))*cos(theta2(t))^2*(diff(theta1(t), t))^2*l1*l2*m2+2*sin(theta1(t))*cos(theta1(t))*cos(theta2(t))^2*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2*m2+2*sin(theta2(t))*cos(theta1(t))^2*cos(theta2(t))*(diff(theta1(t), t))^2*l1*l2*m2-2*cos(theta1(t))^2*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*sin(t)*l1*l2*m2+sin(theta1(t))^2*sin(theta2(t))^2*m2+2*sin(theta1(t))*sin(theta2(t))*cos(theta1(t))*cos(theta2(t))*m2+cos(theta1(t))^2*cos(theta2(t))^2*m2-m1-m2)*l2), diff(diff(theta2(t), t), t) = (4*sin(theta1(t))*sin(theta2(t))*cos(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))^3*(diff(theta2(t), t))*l1^2*l2^3*m2^2-6*sin(theta1(t))*sin(theta2(t))*cos(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))^2*(diff(theta2(t), t))^2*l1^2*l2^3*m2^2+2*sin(theta1(t))*sin(theta2(t))*cos(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))^3*l1^2*l2^3*m2^2-2*sin(theta1(t))*cos(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))^2*(diff(theta2(t), t))^2*sin(t)*l1^2*l2^3*m2^2+2*sin(theta1(t))*cos(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))^3*sin(t)*l1^2*l2^3*m2^2+2*sin(theta2(t))*cos(theta1(t))^2*(diff(theta1(t), t))^2*(diff(theta2(t), t))^2*sin(t)*l1^2*l2^3*m2^2-2*sin(theta2(t))*cos(theta1(t))^2*(diff(theta1(t), t))*(diff(theta2(t), t))^3*sin(t)*l1^2*l2^3*m2^2+sin(theta1(t))^2*sin(theta2(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2^2-sin(theta1(t))*sin(theta2(t))^2*cos(theta1(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2^2+sin(theta1(t))*cos(theta1(t))*cos(theta2(t))^2*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2^2-sin(theta2(t))*cos(theta1(t))^2*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2^2+2*sin(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2*thaw1-2*sin(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2*thaw2-2*cos(theta1(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*sin(t)*l1*l2^2*m2*thaw1+2*cos(theta1(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*sin(t)*l1*l2^2*m2*thaw2+sin(theta1(t))*sin(theta2(t))*l2*m2*thaw1-sin(theta1(t))*sin(theta2(t))*l2*m2*thaw2+cos(theta1(t))*cos(theta2(t))*l2*m2*thaw1-cos(theta1(t))*cos(theta2(t))*l2*m2*thaw2-l1*m1*thaw2-l1*m2*thaw2-2*sin(theta1(t))^2*cos(theta2(t))^2*(diff(theta1(t), t))^3*(diff(theta2(t), t))*l1^2*l2^3*m2^2+4*sin(theta1(t))^2*cos(theta2(t))^2*(diff(theta1(t), t))^2*(diff(theta2(t), t))^2*l1^2*l2^3*m2^2-2*sin(theta1(t))^2*cos(theta2(t))^2*(diff(theta1(t), t))*(diff(theta2(t), t))^3*l1^2*l2^3*m2^2-2*sin(theta2(t))^2*cos(theta1(t))^2*(diff(theta1(t), t))^3*(diff(theta2(t), t))*l1^2*l2^3*m2^2+2*sin(theta2(t))^2*cos(theta1(t))^2*(diff(theta1(t), t))^2*(diff(theta2(t), t))^2*l1^2*l2^3*m2^2-sin(theta1(t))^2*sin(theta2(t))*cos(theta2(t))*(diff(theta2(t), t))^2*l1*l2^2*m2^2+sin(theta1(t))*sin(theta2(t))^2*cos(theta1(t))*(diff(theta2(t), t))^2*l1*l2^2*m2^2-sin(theta1(t))*cos(theta1(t))*cos(theta2(t))^2*(diff(theta2(t), t))^2*l1*l2^2*m2^2+sin(theta2(t))*cos(theta1(t))^2*cos(theta2(t))*(diff(theta2(t), t))^2*l1*l2^2*m2^2-2*sin(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))^2*l1*l2^2*m2*thaw1+2*sin(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))^2*l1*l2^2*m2*thaw2+2*sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))^2*l1*l2^2*m2*thaw1-2*sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))^2*l1*l2^2*m2*thaw2)/(l1*l2^2*(-2*sin(theta1(t))^2*sin(theta2(t))*cos(theta2(t))*(diff(theta1(t), t))^2*l1*l2*m2+2*sin(theta1(t))^2*sin(theta2(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2*m2+2*sin(theta1(t))*sin(theta2(t))^2*cos(theta1(t))*(diff(theta1(t), t))^2*l1*l2*m2-2*sin(theta1(t))*sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*sin(t)*l1*l2*m2-2*sin(theta1(t))*cos(theta1(t))*cos(theta2(t))^2*(diff(theta1(t), t))^2*l1*l2*m2+2*sin(theta1(t))*cos(theta1(t))*cos(theta2(t))^2*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2*m2+2*sin(theta2(t))*cos(theta1(t))^2*cos(theta2(t))*(diff(theta1(t), t))^2*l1*l2*m2-2*cos(theta1(t))^2*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*sin(t)*l1*l2*m2+sin(theta1(t))^2*sin(theta2(t))^2*m2+2*sin(theta1(t))*sin(theta2(t))*cos(theta1(t))*cos(theta2(t))*m2+cos(theta1(t))^2*cos(theta2(t))^2*m2-m1-m2)*m2)}

(4)

````


 

Download freepass2.mw

Use the with(Physics) package to take a derivative of a derivative.

with(Physics):

It appears they used mathematica to build the olympic Velodrom http://www.wolfram.com/customer-stories/key-features-of-mathematica-used-for-the-olympic-velodrome.html

They mention Fresnel integrals, and then it looks like they used an interpolation function (I think that function does what we succeded in doing with Maple back in 2011 - Can we get an exact curve fitting line) to get very good estimates of values without consuming large amounts of calculation time.  Looking further into it I find Track transition curve  which mentions a Euler sprial for the "easement" curve. 

Sorry, that's all I have for you now. 

See the writeto command.  That might be what you're looking for.

Wait, the derivative wrt a derivative?  I think the Physics package diff will do what you want it to do.

with(Physics):

Your dL/d(dq1) will be diff(L,diff(q1(t),t))

and then simply what you had in your original " d (dL/d(dq1)) dt  "  will then just be diff(diff(L,diff(q1(t),t)),t)

I think that is what you are asking.

For display purposes you could do

As Carl said, your request doesn't make much sense (removing 1 element at a time from a sorted list doesn't change the order) ... and removing 19 0's - must be a mistake on your part.  Nonetheless, you could use remove has

for i from 1 to nops(b) do #loop over the number of elements in list b
  a:=remove(has,a,b[i]); #new list of elements in a with element b[i] removed.
end do:

 

Another way

map2(select,a->(a[1]>0),p)

 

If you mean the other value, Maple views numbers in radians but using convert you can go back and forth between degrees and radians ie.  

convert(Pi/4,degrees);

convert(90*degrees,radians);

 

You could also use readdata

readdata("filename",string,2)

remove center from your align commands.  center is not one of the options.

I don't think a seperate package will be developed.  It will be in the works for the Physics package.  But actually I think ecterrab mentioned something to that effect being started at the end of 2016 (not quite 5 years ago). 

 

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