0
$\begingroup$

I have a constructed the Lagrangian of a mechanical system by finding the kinetic and potential energy of the system. Then I tried using EulerEquations to set up a differential equation by taking the variation but seem like it is not working. How to carry out this?

ClearAll["Global`*"];
<< VariationalMethods`
e1 = 0.5*\[Rho]*a*Integrate[(D[W[x, t], {t, 1}])^2, {x, 0, L1}]
e2 = 0.5*Y*Iyy*Integrate[(D[W[x, t], {x, 2}])^2, {x, 0, L1}]
e3 = 0.5*\[Rho]*a*Integrate[(D[U[y, t], {t, 1}])^2, {y, 0, L2}]
e4 = 0.5*Y*a*Integrate[(D[U[y, t], {y, 1}])^2, {y, 0, L2}]
T = e1 + e3;
V = e2 + e4;
Lg = T - V;
EulerEquations[Lg, {W[x, t], U[y, t]}, {x, y, t}]
$\endgroup$
  • $\begingroup$ Lagrangian is written incorrectly. $\endgroup$ – Alex Trounev Jun 3 at 17:53
1
$\begingroup$

If I understand correctly, here should be a system of equations describing the oscillations of the beam. Then Lagrangian and equations have the form

<< VariationalMethods`
e1 = 0.5*\[Rho]*a*(D[W[x, t], {t, 1}])^2;
e2 = 0.5*Y*Iyy*(D[W[x, t], {x, 2}])^2;
e3 = 0.5*\[Rho]*a*(D[U[x, t], {t, 1}])^2;
e4 = 0.5*Y*a*(D[U[x, t], {x, 1}])^2;
T = e1 + e3;
V = e2 + e4;
Lg = T - V;
EulerEquations[Lg, {W[x, t], U[x, t]}, {x, t}]

fig1

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.