Classical Mechanics PHYS 2006 Tim Freegarde 2020 21

Classical Mechanics PHYS 2006 Tim Freegarde 2020 -21 21 Rotating coordinate systems

Classical Mechanics LINEAR MOTION OF SYSTEMS OF PARTICLES centre of mass Newton’s 2 nd law for bodies (internal forces cancel) rocket motion rotations and infinitessimal rotations ANGULAR MOTION angular velocity vector, angular momentum, torque parallel and perpendicular axis theorems rigid body rotation, moment of inertia, precession conservative forces, law of universal gravitation GRAVITATION & KEPLER’S LAWS 2 -body problem, reduced mass planetary orbits, Kepler’s laws energy, effective potential NON-INERTIAL REFERENCE FRAMES NORMAL MODES centrifugal and Coriolis terms Foucault’s pendulum, weather patterns coupled oscillators, normal modes boundary conditions, Eigenfrequencies 2

Rotating coordinate systems • local coordinates not an inertial frame • ‘ficticious’ forces: • centrifugal • Coriolis 3

Rotating coordinate systems ' inertial frame local, rotating frame ' ' • differentiate twice, taking into account variation of local (rotating) unit vectors Coriolis centrifugal 4

Rotating coordinate systems 5

Rotating coordinate systems 6

Rotating coordinate systems 7

Rotating coordinate systems CORIOLIS CENTRIFUGAL 8

Rotating coordinate systems ' inertial frame local, rotating frame ' ' • differentiate twice, taking into account variation of local (rotating) unit vectors Coriolis centrifugal 9

Terrestrial coordinates 10

Rotating coordinate systems xkcd. com 11

Classical Mechanics PHYS 2006 Tim Freegarde