History of variational principles in physics involves integrals over an interval of time and (for fields) extended region of space. Moreover, in the usual formulation of classical action principles, the initial and final states of the system are fixed, e.g., In particular, the fixing of the "final" state appears to give the action principle a teleological character which has been controversial historically. This apparent teleology is eliminated in the quantum mechanical version of the action principle. History of variational principles in physics A variational principle in physics is an alternative method for determining the state or dynamics of a physical system, by identifying it as an
Degrees of freedom (physics and chemistry) Degrees of freedom (physics and chemistry) In physics, a degree of freedom is an independent physical parameter in the formal description of the state of a physical system. The set of all states of a system is known as the system's phase space, and degrees of freedom of the system, are the dimensions of the phase space. A degree of freedom of a physical system is an independent parameter that is necessary to characterize the state of a physical system. In general, a degree of freedom may be any useful property that is not dependent on other variables. The location