sunit

105 Reputation

10 Badges

8 years, 112 days

MaplePrimes Activity


These are replies submitted by sunit

@John Fredsted Thanks a lot sir. But this is not working for the following equation.

restart

junk := (psi*n+1-n*v_SDD)*x[2](T[0], T[1], T[2])+(n*v_SDD-psi*n)*x[2](T[0]-tau_1, T[1], T[2])+2*kappa*(D[1](x[2]))(T[0], T[1], T[2])-2*psi*Pi*k_1+2*kappa*(D[2](x[1]))(T[0], T[1], T[2])+n*v_SDD*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0], T[1], T[2])/(omega_0*psi)-n*v_SDD*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0]-tau_1, T[1], T[2])/(omega_0*psi)+psi*n*(D[2](x[1]))(T[0]-tau_1, T[1], T[2])*tau_1+(D[1, 1](x[2]))(T[0], T[1], T[2])-n*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0], T[1], T[2])/omega_0+omega_0*psi*n*tau[1]*k_1-n*v_SDD*(D[2](x[1]))(T[0]-tau_1, T[1], T[2])*tau_1+n*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0]-tau_1, T[1], T[2])/omega_0+2*(D[1, 2](x[1]))(T[0], T[1], T[2])

(psi*n+1-n*v_SDD)*x[2](T[0], T[1], T[2])+(n*v_SDD-psi*n)*x[2](T[0]-tau_1, T[1], T[2])+2*kappa*(D[1](x[2]))(T[0], T[1], T[2])-2*psi*Pi*k_1+2*kappa*(D[2](x[1]))(T[0], T[1], T[2])+n*v_SDD*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0], T[1], T[2])/(omega_0*psi)-n*v_SDD*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0]-tau_1, T[1], T[2])/(omega_0*psi)+psi*n*(D[2](x[1]))(T[0]-tau_1, T[1], T[2])*tau_1+(D[1, 1](x[2]))(T[0], T[1], T[2])-n*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0], T[1], T[2])/omega_0+omega_0*psi*n*tau[1]*k_1-n*v_SDD*(D[2](x[1]))(T[0]-tau_1, T[1], T[2])*tau_1+n*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0]-tau_1, T[1], T[2])/omega_0+2*(D[1, 2](x[1]))(T[0], T[1], T[2])

(1)

x1sol := R(T[1], T[2])*sin(omega*T[0]+phi(T[1], T[2]))

R(T[1], T[2])*sin(omega*T[0]+phi(T[1], T[2]))

(2)

x1sold := subs(c = omega*T[0]+phi(T[1], T[2]), expand(algsubs(omega*T[0]+phi(T[1], T[2]) = c, map(simplify, subs(T[0] = T[0]-tau_1, x1sol)))))

R(T[1], T[2])*sin(omega*T[0]+phi(T[1], T[2]))*cos(omega*tau_1)-R(T[1], T[2])*cos(omega*T[0]+phi(T[1], T[2]))*sin(omega*tau_1)

(3)

eval(convert(junk, diff), x[1]*(T[0]-tau_1, T[1], T[2]) = R(T[1], T[2])*sin(omega*T[0]+phi(T[1], T[2]))*cos(omega*tau_1)-R(T[1], T[2])*cos(omega*T[0]+phi(T[1], T[2]))*sin(omega*tau_1))

(psi*n+1-n*v_SDD)*x[2](T[0], T[1], T[2])+(n*v_SDD-psi*n)*x[2](T[0]-tau_1, T[1], T[2])+2*kappa*(D[1](x[2]))(T[0], T[1], T[2])-2*psi*Pi*k_1+2*kappa*(D[2](x[1]))(T[0], T[1], T[2])+n*v_SDD*(eval(diff(x[1](t1, T[1], T[2]), t1), {t1 = T[0]-tau_1}))*x[1](T[0], T[1], T[2])/(omega_0*psi)-n*v_SDD*(eval(diff(x[1](t1, T[1], T[2]), t1), {t1 = T[0]-tau_1}))*x[1](T[0]-tau_1, T[1], T[2])/(omega_0*psi)+psi*n*(D[2](x[1]))(T[0]-tau_1, T[1], T[2])*tau_1+(D[1, 1](x[2]))(T[0], T[1], T[2])-n*(eval(diff(x[1](t1, T[1], T[2]), t1), {t1 = T[0]-tau_1}))*x[1](T[0], T[1], T[2])/omega_0+omega_0*psi*n*tau[1]*k_1-n*v_SDD*(D[2](x[1]))(T[0]-tau_1, T[1], T[2])*tau_1+n*(eval(diff(x[1](t1, T[1], T[2]), t1), {t1 = T[0]-tau_1}))*x[1](T[0]-tau_1, T[1], T[2])/omega_0+2*(D[1, 2](x[1]))(T[0], T[1], T[2])

(4)

``

``


Download question3.mw

I tried to substitute for the x[1](T[0],T[1],T[2]), but it is not evaluating.

Please see and help me out for the same,

Regards

Sunit

 

@John Fredsted Sir,

Thanks a lot for helping me out. But just one doubt,will this also work for the following equation.question3.mw

restart

junk := (psi*n+1-n*v_SDD)*x[2](T[0], T[1], T[2])+(n*v_SDD-psi*n)*x[2](T[0]-tau_1, T[1], T[2])+2*kappa*(D[1](x[2]))(T[0], T[1], T[2])-2*psi*Pi*k_1+2*kappa*(D[2](x[1]))(T[0], T[1], T[2])+n*v_SDD*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0], T[1], T[2])/(omega_0*psi)-n*v_SDD*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0]-tau_1, T[1], T[2])/(omega_0*psi)+psi*n*(D[2](x[1]))(T[0]-tau_1, T[1], T[2])*tau_1+(D[1, 1](x[2]))(T[0], T[1], T[2])-n*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0], T[1], T[2])/omega_0+omega_0*psi*n*tau[1]*k_1-n*v_SDD*(D[2](x[1]))(T[0]-tau_1, T[1], T[2])*tau_1+n*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0]-tau_1, T[1], T[2])/omega_0+2*(D[1, 2](x[1]))(T[0], T[1], T[2])

(psi*n+1-n*v_SDD)*x[2](T[0], T[1], T[2])+(n*v_SDD-psi*n)*x[2](T[0]-tau_1, T[1], T[2])+2*kappa*(D[1](x[2]))(T[0], T[1], T[2])-2*psi*Pi*k_1+2*kappa*(D[2](x[1]))(T[0], T[1], T[2])+n*v_SDD*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0], T[1], T[2])/(omega_0*psi)-n*v_SDD*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0]-tau_1, T[1], T[2])/(omega_0*psi)+psi*n*(D[2](x[1]))(T[0]-tau_1, T[1], T[2])*tau_1+(D[1, 1](x[2]))(T[0], T[1], T[2])-n*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0], T[1], T[2])/omega_0+omega_0*psi*n*tau[1]*k_1-n*v_SDD*(D[2](x[1]))(T[0]-tau_1, T[1], T[2])*tau_1+n*(D[1](x[1]))(T[0]-tau_1, T[1], T[2])*x[1](T[0]-tau_1, T[1], T[2])/omega_0+2*(D[1, 2](x[1]))(T[0], T[1], T[2])

(1)

``


Download question3.mw

I need to substitute x[1](T[0]-tau_1,T[1],T[2])=R(T[1],T[2],tau_1)*sin(omega*T[0]+phi(T[1],T[2])). I am asking it, because i tried it but again not performing the subsititution for the 'D'.

 

Thanks a lot sir.

Sunit

 

@dharr Thanks for clarifying it. But cann't we fix the type of data or structure of a defined function?

@dharr Hi,

Thanks for the help. But during running i encountered an issue and thought probably you might help on it. If in the expression for sin if i substitute phi instead of Phi, then map(expand,q) just expanding everything.

I did not get how phi or Phi is making a difference?

@taro Hi, I think i could not pose my question properly. I have to expand sin in terms of omega*T0+phi and T,

something like sin(omega*T0+phi)*cos(T)-sin(T)*cos(omega*T0+phi).

 

@John Fredsted Hi Carl,

I am really thankful for your help. However, i solved it using a little trick. At first i substitute D(lamda)(t-tau_1)=diff(lambda1(t),t) in the expression. After that I put the expression as mentioned above in place of lamda1(t). And it worked.

Thanks

Regards

Sunit

@John Fredsted Hi John,

I am really thankful for putting your effort in my problem. But I think i could not pose my problem properly. Here it is.

I am doing Multiple scale method, and in doing so in one of the steps i am getting D(lamda)(t-tau_1).

Now in further steps, i have to substitute the above mentioned expression  instead of lamda(t-tau_1), and thats why i was asking for the substitution.

I hope this time I made it clear the problem statement.

regards

Sunit

 

 

 

@John Fredsted Yes, tau_1 is same as t_1. Please find the attached sheet.

restart

convert(diff(lambda(t-tau_1), t), diff)

eval(diff(lambda(t1), t1), {t1 = t-tau_1})

(1)

subs(lambda(t-tau_1) = lambda[1](t-tau_1, alpha*t-alpha*tau_1, alpha^2*t-alpha^2*tau_1)+lambda[2](t-tau_1, alpha*t-alpha*tau_1, alpha^2*t-alpha^2*tau_1)*alpha+lambda[3](t-tau_1, alpha*t-alpha*tau_1, alpha^2*t-alpha^2*tau_1)*alpha^2, %)

eval(diff(lambda(t1), t1), {t1 = t-tau_1})

(2)

NULL


Download question2.mw

@John Fredsted Thanks for the help. but my question was for in general.  What if lambda(t-t1) will be

I am really sorry for the confusion, i should have asked  it at the first place.

 

Regards

Sunit

@Doug Meade Thanx for help. But i run the code on maple that you provided and it is giving same result, i.e., neither it is taking out epsilon nor substituting eta(t)=epsilon*z(t).

@Kitonum Thanx and i really appreciate ur help, but please help me for one more thing. When i am trying to multiply two terms under square root like sqrt(a)*sqrt(b) then it is not giving me sqrt(a*b), how to simplify this expression.

 

Regards

Sunit

@Alejandro Jakubi Thanx a lot for helping, but here comes another question. If by default the integration method is cook, then to get correct answer doi have to always use method=nocook whenever i have to integrate a function like  that?

 

Regards

Sunit

@J4James Ok, here it is..

> restart;
> int(BesselJ(1, x), x = 0 .. infinity);
                               -1
> evalf(Int(BesselJ(1, x), x = 0 .. 2500));
                          0.9987629907

Regards

Sunit

@J4James Hi, i m sorry, i just forgot to attach it, here it is. PROBLEM.mw

@Markiyan Hirnyk Thanx for ur suggestion, but i need explicit one as i need to do further manipulation with it..

 

Regards

Sunit

1 2 3 4 5 Page 2 of 5