Summary
- N-dimensional motion can be completely described by n one-dimensional algebraic expressions along n mutually perpendicular directions (where n is any whole number greater than zero).
- Two-dimensional motion can be completely described by two, one-dimensional algebraic expressions along two perpendicular directions.
- Three-dimensional motion can be completely described by three, one-dimensional algebraic expressions along three mutually perpendicular directions.
| r = |
x |
î |
+ |
y |
ĵ |
+ |
z |
k̂ |
| v = |
vx |
î |
+ |
vy |
ĵ |
+ |
vz |
k̂ |
| a = |
ax |
î |
+ |
ay |
ĵ |
+ |
az |
k̂ |
| |
| r2 = |
x2 |
+ |
y2 |
+ |
z2 |
| v2 = |
vx2 |
+ |
vy2 |
+ |
vz2 |
| a2 = |
ax2 |
+ |
ay2 |
+ |
az2 |
| |
| x = |
x(t) |
|
y = |
x(t) |
|
z = |
z(t) |
|
|
| vx = |
∆x |
|
vy = |
∆y |
|
vz = |
∆z |
| ∆t |
|
∆t |
|
∆t |
| ax = |
∆vx |
|
ay = |
∆vy |
|
az = |
∆vz |
| ∆t |
|
∆t |
|
∆t |
| |
| x = |
x(t) |
|
|
y = |
x(t) |
|
|
z = |
z(t) |
|
|
|
| vx = |
dx |
|
vy = |
dy |
|
vz = |
dz |
| dt |
|
dt |
|
dt |
| ax = |
dvx |
= |
d2x |
|
ay = |
dvy |
= |
d2y |
|
az = |
dvz |
= |
d2z |
| dt |
dt2 |
|
dt |
dt2 |
|
dt |
dt2 |
