In
Hamiltonian mechanics
Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) ''momenta ...
, 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 the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sig ...
and
momenta 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.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Ver ...
. 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 continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...
. 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
time
Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...
, 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
Bergmann is a German or Swedish surname. It means "mountain man" in both languages, as well as "miner" in German.
'' Bergman'' is also a common surname in the United States, Sweden, Germany and the Netherlands.
The surname may refer to:
*Art Be ...
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
Further reading
* {{Cite book , last1=Salisbury , first1=D.C. , date=2006 , title=Peter Bergmann and the invention of constrained Hamiltonian dynamics , arxiv=physics/0608067 , bibcode=2006physics...8067S
Hamiltonian mechanics
Theoretical physics