Hamiltonian mechanics In physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (gener ...

, a primary constraint is a relation between the

coordinates In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the Position (geometry), position of the Point (geometry), points or other geometric elements on a manifold such as ...

and

momenta Momenta Global Limited (shortened to Momenta) is a developer of intelligent driving technologies, based in Beijing and Suzhou, China. History Momenta was founded in September 2016 led by Cao Xudong, a former scientist at Microsoft Research a ...

that holds without using the

equations of motion In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathem ...

. A secondary constraint is one that is not primary—in other words it holds when the equations of motion are satisfied, but need not hold if they are not satisfied The secondary constraints arise from the condition that the primary constraints should be preserved in

time Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequ ...

. A few authors use more refined terminology, where the non-primary constraints are divided into secondary, tertiary, quaternary, etc. constraints. The secondary constraints arise directly from the condition that the primary constraints are preserved by

, the tertiary constraints arise from the condition that the secondary ones are also preserved by time, and so on. Primary and secondary constraints were introduced by Anderson and Bergmann and developed by Dirac. The terminology of primary and secondary constraints is confusingly similar to that of first- and second-class constraints. These divisions are independent: both first- and second-class constraints can be either primary or secondary, so this gives altogether four different classes of constraints.

References

* * 2001 reprint by Dover. Footnotes

References

Further reading