The Hamilton function, or Hamiltonian, $H$ of a mechanical system is the Legendre transform of the Lagrange function, $H = \sum_i p_i\dot{q_i} - L$, expressed in terms of the generalized coordinates $q_i$ and their conjugate momenta $p_i$. When the constraints and the potential are independent of time it equals the total energy (kinetic plus potential) of the system, and it accordingly has the dimension of energy.
$H = \sum p_i\dot{q_i} - L$, where $p_i$ is a generalized momentum, $\dot{q_i}$ is a generalized velocity, and $L$ is the Lagrange function.
The Hamilton function, or Hamiltonian, H of a mechanical system is the Legendre transform of the Lagrange function, H = sum_i p_i q_i-dot - L, expressed in terms of the generalized coordinates q_i and their conjugate momenta p_i. When the constraints and the potential are independent of time it equals the total energy (kinetic plus potential) of the system, and it accordingly has the dimension of energy.
Applicable units are those of quantitykind:HamiltonFunction
Hamilton Function