Time-invariant in the context of "Motion"

⭐ In the context of motion, a time-invariant position specifically indicates what state for an object?

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⭐ Core Definition: Time-invariant

In control theory, a time-invariant (TI) system has a time-dependent system function that is not a direct function of time. Such systems are regarded as a class of systems in the field of system analysis. The time-dependent system function is a function of the time-dependent input function. If this function depends only indirectly on the time-domain (via the input function, for example), then that is a system that would be considered time-invariant. Conversely, any direct dependence on the time-domain of the system function could be considered as a "time-varying system".

Mathematically speaking, "time-invariance" of a system is the following property:

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👉 Time-invariant in the context of Motion

In physics, motion is when an object changes its position with respect to a reference point in a given time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed, and frame of reference to an observer, measuring the change in position of the body relative to that frame with a change in time. The branch of physics describing the motion of objects without reference to their cause is called kinematics, while the branch studying forces and their effect on motion is called dynamics.

If an object is not in motion relative to a given frame of reference, it is said to be at rest, motionless, immobile, stationary, or to have a constant or time-invariant position with reference to its surroundings. Modern physics holds that, as there is no absolute frame of reference, Isaac Newton's concept of absolute motion cannot be determined. Everything in the universe can be considered to be in motion.

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Time-invariant in the context of Charge (physics)

In physics, a charge is any of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges correspond to the time-invariant generators of a symmetry group, and specifically, to the generators that commute with the Hamiltonian. Charges are often denoted by ⁠⁠, and so the invariance of the charge corresponds to the vanishing commutator ⁠⁠, where is the Hamiltonian. Thus, charges are associated with conserved quantum numbers; these are the eigenvalues of the generator . A "charge" can also refer to a point-shaped object with an electric charge and a position, such as in the method of image charges.

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LINKED FROM (PARENTS)
← Motion ← Motion (physics) ← Charge (physics)
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Control theory → Function (mathematics) → Dynamical system → System analysis → Time-domain →