Newtonian Dynamics - Constraint Forces

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


\mathbf F=\mathbf F_\parallel+\mathbf F_\perp.

(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

.

(14)

The quantities in (14) are called the internal components of the force vector.

Read more about this topic:  Newtonian Dynamics

Famous quotes containing the words constraint and/or forces:

    In America a woman loses her independence for ever in the bonds of matrimony. While there is less constraint on girls there than anywhere else, a wife submits to stricter obligations. For the former, her father’s house is a home of freedom and pleasure; for the latter, her husband’s is almost a cloister.
    Alexis de Tocqueville (1805–1859)

    There is no longer beauty except in the struggle. No more masterpieces without an aggressive character. Poetry must be a violent assault against the unknown forces in order to overcome them and prostrate them before men.
    Tommaso Marinetti (1876–1944)