Foundations of Relational Particle Dynamics

Understand

Relational particle dynamics include the dynamics of pure shape and cases in which absolute scale or absolute rotation are additionally meaningful.

• These are interesting as regards the absolute versus relative motion debate as well as discussion of conceptual issues connected with the problem of time in quantum gravity.
• In spatial dimension 1 and 2 the relative configuration spaces of shapes are n-spheres and complex projective spaces, from which knowledge I construct natural mechanics on these spaces.
• I also show that these coincide with Barbour's indirectly-constructed relational dynamics by performing a full reduction on the latter.