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'''Lagrangian dynamics''' are an alternative to [[Newtonian mechanics]].  Lagrangian dynamics are particularly useful in solving for the equations of a motion of a system operating under constraints.  Often it is possible, using Lagrangian dynamics, to solve for the equations of motion for a system without needing to solve for the constraint forces, which is why they are often preferred over [[Newtonian mechanics]] for these types of problems.  It is important to note that both methods will yield the same end result, the only thing that changes is the method of arriving at the end result.

'''Lagrangian [[dynamics]]''' are an alternative to [[Newtonian mechanics]].  Lagrangian dynamics are particularly useful in solving for the equations of a motion of a system operating under constraints.  Often it is possible, using Lagrangian dynamics, to solve for the equations of motion for a system without needing to solve for the constraint forces, which is why they are often preferred over [[Newtonian mechanics]] for these types of problems.  It is important to note that both methods will yield the same end result, the only thing that changes is the method of arriving at the end result.

An important concept in Lagrangian mechanics is that of a generalised coordinate, <math>q_k</math>. The position coordinate <math>q_k</math> and corresponding velocity coordinate <math>\dot q_k</math> are taken to be independent of each other so that:

An important concept in Lagrangian mechanics is that of a generalised coordinate, <math>q_k</math>. The position coordinate <math>q_k</math> and corresponding velocity coordinate <math>\dot q_k</math> are taken to be independent of each other so that: