Constraint (classical mechanics)

In classical mechanics, a constraint is a relation between coordinates and momenta (and possibly higher derivatives of the coordinates). In other words, a constraint is a restriction on the freedom of movement of a system of particles. For example, we can say that gas molecules in cylinder are moving irregularly are inside sphere, and have friction(which restrict the freedom of molecules).

Types of constraint

• First class constraints and second class constraints
• Primary constraints, secondary constraints, tertiary constraints, quaternary constraints.
• Holonomic constraints, also called integrable constraints, (depending on time and the coordinates but not on the momenta) and Non-holonomic constraints
• Pfaffian constraints
• Scleronomous constraints (not depending on time) and rheonomous constraints (depending on time).
• Ideal constraints: those for which the work done by the constraint forces under a virtual displacement vanishes.

References

• Goldstein, Herbert; Poole, Charles; Safko, John (2002), Classical Mechanics (3rd ed.), Addison-Wesley, ISBN 978-0-201-65702-9