In
classical mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical m ...
, a constraint on a
system
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expresse ...
is a
parameter
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
that the system must obey. For example, a box sliding down a slope must remain on the slope. There are two different types of constraints:
holonomic and non-holonomic.
Types of constraint
*
First class constraint
A first class constraint is a dynamical quantity in a constrained Hamiltonian system whose Poisson bracket with all the other constraints vanishes on the constraint surface in phase space (the surface implicitly defined by the simultaneous vanish ...
s and
second class constraints
*
Primary constraint
In Hamiltonian mechanics, a primary constraint is a relation between the coordinates and momenta that holds without using the equations of motion. A secondary constraint is one that is not primary—in other words it holds when the equations o ...
s,
secondary constraints,
tertiary constraints,
quaternary constraints.
*
Holonomic constraints, also called integrable constraints, (depending on time and the coordinates but not on the momenta) and
Nonholonomic system
A nonholonomic system in physics and mathematics is a physical system whose state depends on the path taken in order to achieve it. Such a system is described by a set of parameters subject to differential constraints and non-linear constraints, s ...
*
Pfaffian constraints
*
Scleronomic constraints (not depending on time) and
rheonomic constraints (depending on time).
*Ideal constraints: those for which the work done by the constraint forces under a virtual displacement vanishes.
References
Classical mechanics
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