Friday, September 28, 2018

homework and exercises - The relation between Hamiltonian and Energy


I know Hamiltonian can be energy and be a constant of motion if and only if:



  1. Lagrangian be time-independent,

  2. potential be independent of velocity,

  3. coordinate be time independent.


Otherwise $$H\neq E\neq {\rm const},$$ or $$H=E\neq {\rm const},$$ or $$H\neq E={\rm const}.$$


I am looking for examples of these three situation.




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classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

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