Bodies in contact also give rise to * forces of interaction
which can be reduced to the kinematic properties of rigid
conditions. If rigid considered act in a system they force
the particles to move of definite surfaces.
This kind of interaction between particles does not cause
a transition of the notion to the internal, microscopic, degrees
of freedom of bodies. In other words, motion which is limited by
rigid constraints is completely described by its own macroscopic
generalized coordinates qa.
If the limitations imposed by the constraints distort the motion,
they thereby cause acceleration. This acceleration can be
formally attributed to forces which are called reaction forces
of rigid constraints.
Reaction forces charge only the direction of velocity of a particle
but not its magnitude. If they were to alter the magnitude
of the velocity, this would produce a change also in the kinetic
energy of the particle. According to the lawof conservation, of
energy, heat would then be generated. But this was excluded
from consideration from the very start.
to summarize, the reaction forces of ideally rigid
constraints do not change the kinetic energy of the system.
In other words, they do not perform any work on it, since
work performed on a system is equivalent to changing
its kinetic energy.
In order that a force should not perform work, it must be
perpendicular to the displacement. For this reason, the
reaction forces of constraints are perpendicular to the
direction of particle velocity at each given instant of time.
However, in problems of mechanics, the reaction forces are not
* initially given, as are functions of particle position. They
are determined by integrating equations, with account taken of
constraint conditions. Therefore, it is best to formulate the equations
of mechanics so as to exclude constraints reactions entirely. It
turns out that if we go over to generalized coordinates, the
number of which is equal to the number of degrees of freedom
