Previous section: Basic Kinematic Models of Particle Motion.
Next section: Constant Acceleration Model.
Sketch a motion map for the algebraic model: x(t) = x0 + vt
[Note that including the origin or coordinates in the map introduces arbitrary and unnecessary complications.]
This is really the same equation as the parametric equation in exercise (2) of High School Geometry with GA
for a straight line, x(α) = a + αu. We've just used t (for time) as our parameter name here and changed the names
of the constant vectors. The link to Solutions for the exercises on that page shows an interactive diagram.
Derive a nonparametric equation for this model, and relate it to angular momentum.
Again, we could refer to the link mentioned in the previous paragraph, where the exercises started with a
nonparametric equation. We can get back to that kind of form by wedging our equation above on both
sides by the constant velocity v. But, we may as well wedge with mv so that we see the relationship to
angular momentum:
x(t)∧(mv) = x0∧(mv)
That is, the angular momentum of the free particle at any time is a bivector with the same orientation and
value as the initial angular momentum bivector. These bivectors can also be seen as the blue and green
bivectors in the interactive diagram referred to above, where the diagram's vector a is replaced by our x0
and the diagram's vector u is replaced with mv.
Previous section: Basic Kinematic Models of Particle Motion.
Next section: Constant Acceleration Model.