Analytical mechanics

The traditional mechanical can be written (formalized) in various manners. Most current is the formulation of Newton, which uses the concept of force: it is simplest by far when it is a question of considering a concrete problem and this is why it is that which is taught. But to be able to deal with more complex problems or more finely, and to be able to make rigorous demonstrations, this formulation is not most practical.

The analytical mechanics , initiated as of the XVIIIe century, gathers thus various mathematized formulations very of traditional mechanics, in particular mechanics of Hamilton and Lagrange. Once again, all these formulations are equivalent.

Principle of Alembert

Mechanical of Lagrange | Not of Lagrange

Mechanical of Hamilton | Equations of Hamilton-Jacobi

symplectic Variety | symplectic Geometry

Symmetries and laws of conservation

The tools making it possible to deal with these problems are, inter alia:

curvilinear integral
the Hamiltonian vector fields

See also: Physical | Mechanical quantum | Mechanical of the fluids

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