dynamic variable

physics

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June 25, 2026

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In physics, a "dynamic variable" refers to a quantity that changes over time within a system. These variables are essential for describing the motion and evolution of physical systems.

In classical mechanics, dynamic variables include position and momentum, which are governed by Newton's laws of motion. More advanced formulations, like Lagrangian mechanics and Hamiltonian mechanics, use concepts like generalized coordinates and momenta to describe these dynamic variables.1

In contrast, quantum mechanics introduces the idea of inherent randomness, where probabilities, rather than definite values, are predicted for dynamic variables. This concept of "hidden variables" has been explored as a way to restore determinacy but is not widely supported. The Schrödinger equation describes how these dynamic variables, represented by wave functions, change over time in quantum systems.23

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mechanics
Configuration space
…to reduce the number of dynamic variables in a problem (the x, y, and z coordinates of each particle) to a smaller number of generalized dynamic variables, which need not even have the same dimensions as the original ones.
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…to reduce the number of dynamic variables in a problem (the x, y, and z coordinates of each particle) to a smaller number of generalized dynamic variables, which need not even have the same dimensions as the original ones.
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mechanics
Lagrange’s and Hamilton’s equations
…a dynamic problem has six dynamic variables for each particle—that is, x, y, z and ẋ, ẏ, ż—and the Lagrangian depends on all 6N variables if there are N particles.
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…a dynamic problem has six dynamic variables for each particle—that is, x, y, z and ẋ, ẏ, ż—and the Lagrangian depends on all 6N variables if there are N particles.
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mechanics
Motion of a pendulum
In the first case, the dynamic variable (meaning the quantity that changes with time) is θ, in the second case it is x. In both cases, the second derivative of the dynamic variable with respect to time is equal to the variable itself multiplied by a negative constant. The equations…
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In the first case, the dynamic variable (meaning the quantity that changes with time) is θ, in the second case it is x. In both cases, the second derivative of the dynamic variable with respect to time is equal to the variable itself multiplied by a negative constant. The equations…
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