Identify the generalized coordinate of the system, .

Generalized coordinates and forces, Lagrange's equations.

Generalized coordinates: The variables describing the pose of the mobile platform.

where q is a vector consisting of the generalized coordinates.

where m indicates the total number of generalized coordinates.

where the qi are generalized coordinates and the Qi are generalized forces.

The degrees of freedom xn are coordinates on the phase space of the system and are therefore commonly subdivided into generalized position coordinates qk and generalized momentum coordinates pk, where pk is the conjugate momentum to qk.

In analytical mechanics, the configuration space is the generalised 6N coordinate space of the position and velocity of a mechanical system described by the Lagrange equations.

These 6N dimensions correspond to the generalised and canonically conjugate variables of the mechanical system in question.

Applying a vector conversion from the Cartesian coordinates to the generalized coordinates will describe the same three-dimensional structure using the Flory convention.

In modeling the position vectors of atoms in macromolecules it is often necessary to convert from Cartesian coordinates (x,y,z) to generalized coordinates.

More generally, for N particles in an arbitrary generalised coordinate system we will have, in matrix notation:

If the transformation equations defining the generalized coordinates are independent of t, it can be shown that H is equal to the total energy E = T + V.

For an arbitrary choice of generalized coordinates, it may not be possible to obtain an intuitive interpretation of the conjugate momenta.

In general, when the system obeys Lagrangian mechanics, its state can be described using generalized coordinates.