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holonomic constraints : ウィキペディア英語版
holonomic constraints
In classical mechanics, holonomic constraints are relations between the position variables (and possibly time) which can be expressed in the following form:
f(q_1, q_2, q_3,\ldots, q_, t) = 0, where \ are the n coordinates which describe the system. For example, the motion of a particle constrained to lie on the surface of a sphere is subject to a holonomic constraint, but if the particle is able to fall off the sphere under the influence of gravity, the constraint becomes non-holonomic.
Velocity-dependent constraints such as
f(q_,q_,...,q_,\dot_,\dot_,...,\dot_,t)=0
are not usually holonomic.
==Holonomic system (physics)==
In classical mechanics a system may be defined as holonomic if all constraints of the system are holonomic. For a constraint to be holonomic it must be expressible as a function:
: f(x_1,\ x_2,\ x_3,\ \dots,\ x_N,\ t)=0, \,
i.e. a holonomic constraint depends only on the coordinates x_j\,\! and time t\,\! . It does not depend on the velocities. A constraint that cannot be expressed in the form shown above is a nonholonomic constraint.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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