Phase space coordinates (p, q) and Hamiltonian H
Let $${\displaystyle (M,{\mathcal {L}})}$$ be a mechanical system with the configuration space $${\displaystyle M}$$ and … See more

Hamilton's equations can be derived by a calculation with the Lagrangian $${\displaystyle {\mathcal {L}}}$$, generalized positions q , and generalized velocities , where See more

• The value of the Hamiltonian $${\displaystyle {\mathcal {H}}}$$ is the total energy of the system if and only if the energy function $${\displaystyle E_{\mathcal {L}}}$$ has the same property. (See definition of $${\displaystyle {\mathcal {H}}}$$ See more

In its application to a given system, the Hamiltonian is often taken to be
where $${\displaystyle T}$$ is the kinetic energy and $${\displaystyle V}$$ is the potential energy. … See more

A sufficient illustration of Hamiltonian mechanics is given by the Hamiltonian of a charged particle in an electromagnetic field. In See more

Geometry of Hamiltonian systems
The Hamiltonian can induce a symplectic structure on a smooth even-dimensional manifold M … See more

• Canonical transformation
• Classical field theory
• Hamiltonian field theory
• Covariant Hamiltonian field theory See more