Speaker: Professor Tony Bloch (U-M Mathematics)
Professor Bloch will discuss some of the physics and mathematics of the classical motion of rigid bodies and general mechanical systems. The basic principle underlying most dynamics is the principle of least action. He will discuss some of the history of this principle and how it gives rise to motion of particles and rigid bodies. He will describe important related concepts such as the role of symmetry and the conservation of angular momentum and energy. For bodies, which roll or skate a more general principle, the Lagrange-D'Alembert principle, must be used to obtain the dynamics. In such cases, angular momentum is not necessarily conserved and one obtains rich and sometimes surprising dynamics. Professor Bloch will give examples of rotating bodies that spontaneously change their direction of motion and that can proceed uphill without the application of outside force.