Now consider the motion of a point in a 3D world
. Imagine that a geometric model, as defined in Section 3.1, is moving over time. This causes each point
on the model to move, resulting a function of time for each coordinate of each point:
![$\displaystyle (x(t),y(t),z(t)) .$](img711.gif) |
(8.8) |
The velocity
and acceleration
from Section 8.1.1 must therefore expand to have three coordinates. The velocity
is replaced by
to indicate velocity with respect to the
,
, and
coordinates, respectively. The magnitude of
is called the speed:
![$\displaystyle \sqrt{v_x^2 + v_y^2 + v_z^2}$](img713.gif) |
(8.9) |
Continuing further, the acceleration also expands to include three components:
.
Steven M LaValle
2020-11-11