| THERMO Spoken Here! ~ J. Pohl © ( A4340~3/15) | ( A4380 - 1.18 Value, Slope and Curvature) |
It is helpful to use simple but effective vector notations with beginning thermodynamic analyses. Much can be made clear by use of mathematical notation. The table presents some representations of position and velocity (of a BODY).
Prior to writing a vector, an origin must be selected and coordinates affixed. It is wise to orient coordinates in a convenient manner; take the time to do so. To the chosen coordinates, affix unit vectors as its basis. The example notations below are for an 0XZ coordinate reference with I and K as the unit vector basis. A "Y" coordinate with its unit vector, "J" can be added quite easily. To save writing, that coordinate is omitted.
The location (position) of a "BODY" in space is synonymous with the location of a "point" in space.
| Position of a BODY (verbal, physical description) |
Position of a BODY (mathematical description) |
| Definite position: | PBODY = aI + cK, where "a" and "c" are numbers. |
| Indefinite Position: | Ppoint = x* I + z*K |
| Changing Position: | P(t)BODY = x(t) I + z(t) K and at the origin at time, t = 0+. P(t)BODY = (x(t) + x0)I + (z(t) + z0)K at x0 and z0 at t = 0+. |
| Initial Condition: Zero Velocity Motion |
Position: P = P0+ or P0+ = x0+I + z0+K. Velocity: Vo+ = 0 |
| Initial Condition: Constant Velocity Motion |
Position: P(t) = P0+ + V0+t Velocity: V = Vo+ or V0+ = vx,0+ I + vz,0+ K |
In addition some graphic or sketch of the system, showing the space, the origin reference, orthogonal coordinates and unit vectors, is needed. It is awkward to discuss vectors in a general way. More about vectors will be presented in the specific contexts of text examples. Persons familiar with vectors can bypass the detail; beginners should not.
Some say position and velocity are system "characteristics," not properties. It is helpful to use simple but effective vector notations with beginning mechanics and thermodynamic analyses. The table presents some representations of position and velocity (of a BODY or a Point).
Premise presently unwritted!