A system with two degrees of freedom has the Lagrangian [L=dot{q}_{1}^{2}+alpha dot{q}_{1} dot{q}_{2}+beta q_{2}^{2} / 2,] where

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A system with two degrees of freedom has the Lagrangian

\[L=\dot{q}_{1}^{2}+\alpha \dot{q}_{1} \dot{q}_{2}+\beta q_{2}^{2} / 2,\]

where $\alpha$, and $\beta$ are constants. Find the Hamiltonian, identify any conserved quantities, and write out Hamilton's equations of motion.

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Modern Classical Mechanics

ISBN: 9781108834971

1st Edition

Authors: T. M. Helliwell, V. V. Sahakian

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Question Posted: Mar 21, 2024 12:01 AM

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A system with two degrees of freedom has the Lagrangian [L=dot{q}_{1}^{2}+alpha dot{q}_{1} dot{q}_{2}+beta q_{2}^{2} / 2,] where

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Modern Classical Mechanics

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