Mechanics 1

Mathematical preliminaries


Vector manipulation




Kinematics of the material point


Kinematics and relativity of motion / observer


Reference frames and frames of reference


Linked vectors


Velocity and acceleration


Time derivation of vectors


Coordinate systems coordinate systems


Intrinsic coordinates


Examples of motion




Changes of reference frame in classical mechanics


Composition of velocities


Compositions of accelerations




Dynamics of the material point


Newton's three laws.


Notion of force.


Notion of Galilean reference frame.


Quantity of motion of a material point


Descriptions of different interactions (resultant, point of application)


Importance of Newton's third law in the case of several interacting objects




Energy of the material point


Elementary displacement


Power and work of a force.


Law of kinetic energy and law of kinetic power in a Galilean frame of reference.


Law of mechanical energy and law of mechanical power in a Galilean frame of reference.


potential energy. mechanical energy.


Conservative and non-conservative forces.




One-degree-of-freedom oscillator


Damped and undamped oscillator, free-running or forced sinusoidal.


Applications to point mechanics: the case of the heavy pendulum and the mass-spring system.




Kinetic moment theorem for the material point


Introduction to the various concepts related to rotation by analogy with translation


Equation of the simple pendulum based on the kinetic moment theorem.


Law of transport of kinetic moment and the moment of a force.