Dependent Motion

Non-Uniform Motion (Dependent Motion)

When a force⁶ acts upon uniform motion, that motion begins to vary in time (Δv/Δt), resulting in speeding up (acceleration) or slowing down (deceleration). The common term is accelerated motion for both cases—a consistent change in velocity over a period of time. All waves are accelerated motions, including simple, harmonic motion:

A form of periodic motion of a particle, etc, in which the acceleration is always directed towards some equilibrium point and is proportional to the displacement from this point.⁷

Accelerated motions require at least TWO other motions to maintain their behavior, whether periodic or not. For example, if you have a car moving at a constant velocity down the highway (uniform motion), all the other related motions (seats, occupants, etc) are dependent upon the car, but cannot change from that constant velocity unless another motion is introduced, such as stepping on the gas or turning a corner. Therefore:

1. Any motion derived from a single, uniform motion will act in unison with the uniform motion. There can be no change in linear or angular velocity.⁸

2. Any motion derived from a combination of two or more motions can change its velocity, accelerate or vibrate.

These non-uniform motions will be referred to as dependent motions, as they are dependent upon either a uniform motion or another dependent motion to maintain integrity.

The relationship between uniform and dependent motions can be expressed graphically:

The fundamental motions are the uniform motions, which are called the “scalar motions” in Larson's Reciprocal System of theory. However, Larson only considers the linear form of uniform motion in his analysis. RS2, the reevaluation of the Reciprocal System, considers both linear and angular aspects of uniform motion in its structure.