(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the Hamiltonian and Hamilton's equations of motion for a system with two degrees of

freedom with the following Lagrangian

L = 1/2m_{1}[itex]\dot{}xdot[/itex]_{1}^{2}+ 1/2m_{2}[itex]\dot{}xdot[/itex]_{2}^{2}+ B_{12}[itex]\dot{}xdot[/itex]_{1}x_{2}+ B_{21}[itex]\dot{}xdot[/itex]_{1}x_{1}- U(x_{1}, x_{2})

Explain why equations of motion do not depend on the symmetric part of B_{ij}.

2. Relevant equations

3. The attempt at a solution

No problem finding the Hamiltonian and the e.o.m. The last part is the problem. All I can think of is that the symmetric part is diagonalised to become the mass, since in general for a lagrangian you have L = 1/2 a_{ij}(q)[itex]^{}qdot[/itex]^{2}

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# Hamiltonian question

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