Università Roma Tre

Teaching unit I – Fundamental tools and methods
Elements of vector algebra
Rotation matrix
ODE homogeneous and non-homogeneous
Spectral analysis of symmetric matrices
Eigenvalues problem and diagonalization
Conservative, potential and irrotational vector fields
Teaching unit II – Mechanics of a material particle
Fundamental properties of the motion of a particle
Dynamics of free and constrained material elements
Un-damped and damped oscillators
Mechanical work, power and energy
Stabilty of mechanical equilibrium
Teaching unit III – Mechanics of systems of particles
Internal forces
Conservation of momentum
Conservation of angular momentum
Kinetic energy, Koenig’s theorem
Teaching unit IV – Rigid-body motion and Galilean relativity
Two- and Three-dimensional rigid-body motion
Kinematics in non-inertial frames of reference
Dynamics in non-inertial frames of reference, fictitious forces
Derivative of vectors in moving frames of reference
Trasformazioni tra riferimenti in moto relativo
Derivata temporale di R
Teaching unit V – Statics and dynamics of rigid bodies
Dynamics
Conservation of momentum and angular momentum
Inertia tensor
Ellipsoid of inertia
Koenig’s theorem
Euler equations
Rotation about central axes
Gyroscopes and precessions
Statics
Equivalent forces
Central axis of a system of forces
Constraints reactions
Graphic methods for the analysis of equilibrium
Teaching unit VI – Elements of Lagrangean mechanics

• Lecture notes with solved problems