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docs/physics/classical-mechanics/hamiltonian-mechanics/hamiltonian-formalism.md
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# Hamiltonian formalism of mechanics
The Hamiltonian formalism of mechanics is based on the definitions posed by [Lagrangian mechanics](/en/physics/mechanics/lagrangian-mechanics/lagrangian-formalism) and the axioms, postulates and principles posed in the [Newtonian formalism](/en/physics/mechanics/newtonian-mechanics/newtonian-formalism/).
The Hamiltonian formalism of mechanics is based on the definitions posed by [Lagrangian mechanics](../lagrangian-mechanics/lagrangian-formalism.md) and the axioms, postulates and principles posed in the [Newtonian formalism](../newtonian-mechanics/newtonian-formalism.md).
Where the Lagrangian formalism used the [principle of virtual work](/en/physics/mechanics/lagrangian-mechanics/lagrange-equations/#principle-of-virtual-work) to derive the Lagrangian equations of motion, the Hamiltonian formalism will derive the Lagrangian equations with the stationary action principle. A derivative of Fermat's principle of least time.
Where the Lagrangian formalism used the [principle of virtual work](../lagrangian-mechanics/lagrange-equations.md#principle-of-virtual-work) to derive the Lagrangian equations of motion, the Hamiltonian formalism will derive the Lagrangian equations with the stationary action principle. A derivative of Fermat's principle of least time.
In Hamilton's formulation the stationary action principle is referred to as Hamilton's principle.