
#1
Jan1712, 04:13 PM

P: 275

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} 


Register to reply 
Related Discussions  
A question regarding a Hamiltonian.  Quantum Physics  5  
Commutator of the Hamiltonian with Position and Hamiltonian with Momentum  Advanced Physics Homework  2  
quantum question  hamiltonian  Introductory Physics Homework  1  
Question concerning Hamiltonian and eigenstates  Advanced Physics Homework  0  
Lagrange and Hamiltonian question  Introductory Physics Homework  6 