Course information

Introduction to Basic Mathematical Tools: Vectors and vector operations. Inner-outer product. Vector derivatives. Velocity - acceleration. Series expansion. Vectors and polar coordinates. Newton s Laws for the motion of bodies: Newton s Laws. Forces and equations of motion. Motion in a homogeneous field. Newton s Law of Universal Gravitation. Motion in a constant electric (or magnetic) field. Momentum conservation. Friction forces. Reference Systems –Galileo Transformations: Inertial and accelerated reference systems. Absolute and relative acceleration, Hypothetical forces. Absolute and relative velocity – Galileo Transformation. Momentum conservation - Collisions. Velocity and acceleration in rotating reference systems. Lorentz Transformations: Derivation of Transformations. Proper length – Proper time, Contraction – Dilation. Velocity transformations according to Lorentz: Derivation of Transformations. Relativistic dynamics: Mass transformation. Energy Conservation: Work - Energy. Kinetic energy - Potential energy. Conservative Forces - (Electric, Gravitational, Escape Velocity). Power of variable force. Conservation of Momentum and angular momentum: Internal forces and conservation of momentum. Center of mass - Collisions. Systems with variable mass. Angular momentum with respect to the center of mass. Law of change of angular momentum. Harmonic Oscillator: Spring - mass, simple pendulum, LC circuit. Average kinetic and potential energy. Harmonic oscillator with damping. Elementary Dynamics of Rigid Bodies: Equation of motion of a rigid body. Angular momentum and kinetic energy. Moment of inertia - Theorems of parallel / perpendicular axes. Rotation around a fixed axis - Dependence of motion on time. Rotation around a fixed axis - Behavior of angular momentum. Central Forces - Inverse Square Forces: Force between a point mass and a spherical shell / solid sphere. Orbits around an attractive center - Kepler s Laws. The problem of two bodies - Reduced mass.