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Luc Bijl 2025-08-28 17:12:46 +02:00
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docs/physics/classical-mechanics/hamiltonian-mechanics/equations-of-hamilton.md
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@ -78,7 +78,7 @@ To put it differently; a Hamiltonian of a conservative autonomous system is cons
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It may be observed that the Hamiltonian $\mathcal{H}$ and [generalised energy](/en/physics/mechanics/lagrangian-mechanics/lagrange-generalizations/#the-generalized-energy) $h$ are identical. Note however that $\mathcal{H}$ must be expressed in $(\mathbf{q},\mathbf{p},t)$ which is not the case for $h$.
It may be observed that the Hamiltonian $\mathcal{H}$ and [generalised energy](../lagrangian-mechanics/lagrange-generalizations.md#the-generalized-energy) $h$ are identical. Note however that $\mathcal{H}$ must be expressed in $(\mathbf{q},\mathbf{p},t)$ which is not the case for $h$.
> *Proposition 2*: a coordinate $q_j$ is cyclic if
>

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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.