This equation is related to classical equation for electrical power:

This result is again in accord with the classical equation.

The only known analytic solutions to the classical equations of motion are marginal deformations.

As the relevant speeds increase toward the speed of light, acceleration no longer follows classical equations.

Using the classical equation for conservation of energy of a particle:

For example, an electron around an atom does not emit radiation in the pattern predicted by these classical equations.

With the advent of general relativity, the classical equations of motion became modified.

All classical equations of motion can be derived from this variational principle:

The classical equations of motion can be written in terms of the Hamiltonian, even for highly complex or abstract systems.

Demanding that the classical equations of motion are preserved is not a strong enough condition to determine the matrix elements.