# Maths Theory/Mechanics

__Basic Mechanics__

__Constraints__

When there are constraints, the coordinates are no longer independent - they are connected by the equations of constraint.
The procedure is to introduce generalized coordinates.

__Lagrange's Equation__

__Hamilton's Principle__

__Calculus of Variations__

The problem is to find the curve for which some given line integral has a stationary value.
For an action

the condition for a stationary value is equivalent to Lagrange's Equation

__Advantages of Variational Principles__

At its most useful when a Lagrangian of independent coordinates can be set up.
It contains all the mechanics of holonomic systems with forces derivable from potentials.

Further it involves only physical quantities that can be defined without reference to a set of generalized coordinates. It is therefore automatically invariant with respect to whatever coordinates are used.