Nondynamical

Nondynamical is an adjective used in physics, mathematics, and related fields to describe variables, components, or systems that do not change with time under the dynamics being considered. It contrasts with dynamical quantities, which evolve according to equations of motion or evolution laws. The term is often applied to parameters, constraints, or fields that are held fixed or do not possess a kinetic term in a Lagrangian or Hamiltonian formulation.

In physics, a nondynamical variable may be a Lagrange multiplier enforcing a constraint, an external field treated as prescribed rather than evolved, or a parameter that remains constant during the analysis. In a dynamical system, such variables are not integrated over time; instead they appear as fixed inputs or algebraic conditions. In some cases, nondynamical fields can be eliminated algebraically, yielding a reduced or effective theory.

Note differences with terms like static, time-independent, or equilibrium. While statics refer to absence of motion in a physical sense, nondynamical refers specifically to the role of a quantity within a dynamical framework. A quantity can be nondynamical yet fluctuate statistically if the underlying framework is stochastic; conversely a variable can be time-dependent in one model but treated as nondynamical (frozen) in another.

Applications span mechanics, constrained systems, and field theory where auxiliary fields or multipliers are treated as nondynamical; in control theory, parameters that do not have their own dynamics may also be described this way. The usage of nondynamical is more common in technical discussions of models with both evolving and non-evolving components, rather than in everyday language.