Constraint Forces
For a constrained Newtonian dynamical system the constraints described by the equations (6) are usually implemented by some mechanical framework. This framework produces some auxiliary forces including the force that maintains the system within its configuration manifold . Such a maintaining force is perpendicular to . It is called the normal force. The force from (6) is subdivided into two components
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.(13)
The first component in (13) is tangent to the configuration manifold . The second component is perpendicular to . In coincides with the normal force .
Like the velocity vector (8), the tangent force has its internal presentation
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.
(14)
The quantities in (14) are called the internal components of the force vector.
Read more about this topic: Newtonian Dynamics
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