MATH 213: Mechanics II (Mechanics of Particles Systems and Rigid-Bodies)
3 Cr. Hr. (L3+Sc 1)
Prerequisite : (MATH 112)
1. Particles dynamics in two and three dimensions: Constrained particle motion( Motion on a circle and on a cycloid) - Orbital motion. 2. Motion of a System of Particles: Linear momentum of a system of particles - Angular momentum - Use of centroid - Moving origins. 3. Kinematics of a rigid body rotating about a fixed point: Vector angular velocity - Composition of angular velocities - Moving axes - Orthogonal transformations -Instantaneous axis of rotation and instantaneous center of rotation. 4. Introduction to Rigid-body dynamics: Moments and products of inertia - The theorem of parallel and perpendicular axes - Angular momentum of a rigid body about a fixed point and fixed axes - Principal axes - Momental ellipsoid – equimomental systems - Kinetic energy of a rigid body rotating about a fixed point. 5. Two-Dimensional Rigid Body Dynamics: Newton’s laws of motion - Conservation of angular momentum - Conservation of energy - Impulsive motion Three-Dimensional Rigid Body Dynamics: Euler’s equations of motion - Motion of a rigid body under no forces - Eulerian angles - Motion of a symmetrical top - General three-dimensional rigid body motion - Accelerated coordinate systems(Coriolis force) - Application to earth rotation - Motion of rigid bodies in contact.