There are four basic states of any type of motion . They are:
- Static (no motion) – This is the state of matter that we commonly associate with geometry and structures in general. As shown previously in this book, it is a concept of being that is disassociated with time and more of a theoretical concept than it is an actual state of (non) ‘motion’. V = 0
- Velocity – Velocity is the state wherein an object has a constant relationship with time. This pretty well applies to all matter, rather than being some sort of theoretical state. Since there can be no preferred reference system (no motion vector that is considered universal), it is considered to be a relative value. (More on this later.) V = l/t
- Acceleration – Acceleration is the type of motion where the velocity is changing, either in magnitude or direction. It is commonly expressed in units of distance or rotation versus time squared. Force is also expressed in these units. A = l/t2 = V/t
- Jerk – There is a state of motion not commonly used in calculations called Jerk. Jerk is the name for the situation in which the acceleration itself is changing over time, commonly experienced when an elevator starts up or slows down, or in a carnival ride like a Tilt-a-Whirl. J = l/t3 = A/t = V/t2
In the past, we have chosen to make our primary measurements in the Static realm because of tradition and the belief that it makes the calculations easier, but other choices can be just as valid and can also be used to calculate the other state values.
Suppose, for example that we decided to make our primary measurements in the acceleration realm, as we might do when combining forces. The time squared in the denominator would then be understood as a constant, because all measurements would be expected to be made in this realm.
One could readily deduce velocity from these measurements by knowing the initial velocity and (in the more general case where the acceleration itself could change), integrating the acceleration over time. The mathematical expression for this is shown below.
V = ∮a dt + V0
Similarly, one could calculate the position by integrating the velocity over time, and knowing the starting position. We won’t go any deeper into those mathematics at this point (or ever, in this book) and to see the derivation a full methodology, consult any book or source regarding Dynamics. But I think that you can see that by making the primary measurement in the acceleration realm, details such as location become more difficult to obtain, requiring multi-level calculations.
So it is currently with velocity. In a Cartesian system, because of the structure of the measurement system, one must go through the second order equations of the Pythagorean Theorem to calculate the desired result. However, if one chooses to measure velocity directly, this problem is eliminated and the velocity calculations all become first order.
With velocity as the primary measurement, location becomes a little harder to calculate, but frankly, that is how it should be, because a true time-function location is difficult to measure (as Quantum Mechanics has shown). But the acceleration state becomes more accessible since it is only one time-state up from the primary measurement. As we shall see in later chapters, this is very useful.
So in choosing a fundamental measurement concept, it would seem to be important to choose one that can most easily express the most common state of the components of the surrounding universe. One that lends itself easily to expressing the state of the matter involved.