In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other … See more

Notation
Boldface variables such as $${\displaystyle \mathbf {q} }$$ represent a list of See more

When the problem allows additive separation of variables, the HJE leads directly to constants of motion. For example, the time t can be separated if the Hamiltonian does … See more

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• Canonical transformation
• Constant of motion See more

The Hamilton–Jacobi equation is a first-order, non-linear partial differential equation
for a system of particles at coordinates $${\displaystyle \mathbf {q} }$$. The function See more

The Hamilton–Jacobi equation is a single, first-order partial differential equation for the function of the $${\displaystyle N}$$ generalized coordinates See more

Optical wave fronts and trajectories
The HJE establishes a duality between trajectories and wavefronts. For example, in geometrical … See more