What is constraint equation?

In mechanics, a constraint algorithm is a method for satisfying constraints for bodies that obey Newton's equations of motion. There are three basic approaches to satisfying such constraints: choosing novel unconstrained coordinates ("internal coordinates"), introducing explicit constraint forces, and minimizing constraint forces implicitly by the technique of  projection methods.

Constraint algorithms are often applied to molecular dynamics simulations. Although such simulations are sometimes carried out in internal coordinates that automatically satisfy the bond-length and bond-angle constraints, they may also be carried out with explicit or implicit constraint forces for the bond lengths and bond angles. Explicit constraint forces typically shorten the time-step significantly, making the simulation less efficient computationally; in other words, more computer power is required to compute a trajectory of a given length. Therefore, internal coordinates and implicit-force constraint solvers are generally preferred.