Free Particle Model

Previous section: Basic Kinematic Models of Particle Motion.

Next sectionConstant Acceleration Model.


Sketch a motion map for the algebraic model:    x(tx0 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) 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)(mvx0(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 sectionBasic Kinematic Models of Particle Motion.

Next section: Constant Acceleration Model.

© David Hestenes 2005, 2014