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When does the total time derivative of the Hamiltonian equal its partial time derivative?
When does the total time derivative of the Hamiltonian equal the partial time derivative of the Hamiltonian? In symbols, when does $\frac{dH}{dt} = \frac{\partial H}{\partial t}$ hold?
In Thornton &...
- 935
2
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1
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Hamiltonian time-independent, partial derivative always zero?
For conceptual simplicity, let's restrict the discussion to systems with a two-dimensional phase space $\mathcal P$ with generalized coordinates $(q,p)$.
Hamiltonian is a function that maps a pair ...
- 51
2
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The definition of the hamiltonian in lagrangian mechanics
So going through the "Analytical Mechanics by Hand and Finch". In section 1.10 of the book, the Hamiltonian $H$ is defined as: $$H = \sum_k{\dot{q_k}\frac{\partial L}{\partial \dot{q_k}} -L}.\tag{1.65}...
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