Newtonian Dynamics PC

This course is partly intended to generalize the knowledge acquired during the first semester of the first year (General Physics). In this perspective, we will deal with the location in a three-dimensional space, the associated kinematics and the mechanics in a non-galilean frame of reference. This course is also intended to broaden the scope of applications covered in L1S1. In this respect, the statics of fluids, the dynamics and energetics of the harmonic oscillator, and the motion of celestial bodies (Kepler's laws) will be covered.

At the end of the cycle, a student must be able to predict qualitatively the evolution of usual mechanical systems and to understand their energetic behavior. He/she should be able to conduct a complete quantitative analysis within the framework of a simplified model of the system studied.

This course is intended for students who have already completed the first year of university education. Students who take this course must have a good command of the following mathematical tools: Trigonometric formulas, complex numbers (real part, imaginary part, modulus and argument) scalar product, functions of one real variable, derivative, primitive, limited development to the first order and differential equations.

Recommended Prerequisites*: Vector product, mixed product and the necessary notions on functions of several variables, partial derivatives and systems of differential equations will be explicitly covered in the course and are therefore not required a priori.

CC + final exam. Grade = Max (0.3*CC+ 0.7*ET)

CH I COORDINATE SYSTEMS IN 3D

• Reference frame and reference of an observer
• Different coordinate systems
• Coordinated surfaces and lines

CH II PHYSICAL QUANTITIES

• Scalar and vector quantities
• Colinear and coplanar vectors and decomposition bases
• Construction of the local base associated with a coordinate system
• Scalar product and different expressions of the position vector

CH III DIFFERENTIAL AND INTEGRAL CALCULUS

• Displacement vector and elementary displacement
• Integral calculus, application to length calculations
• Vector product, elementary surface vector and area calculations
• Mixed product, elementary volume and volume calculations

CH IV GRADIENT OPERATOR

• Gradient of a scalar field
• Establishment of the form
• Circulation of a vector field
• Conservative forces and potential energy

CH V FLUID STATICS

• Scalar field of pressures
• Fundamental equation of fluid statics
• Archimedean thrust

CH VI : HARMONIC OSCILLATOR

• Ideal oscillator
• Damped oscillator
• Forced oscillator

CH VII THE CINETIC MOMENT THEOREM

• Reminder of point mechanics
• Theorem of angular momentum
• Central force movement
• Celestial mechanics: Kepler's three laws

CH VIII CHANGE OF REFERENCES

• Law of composition of positions
• Characterization of the motion of the relative reference frame in the absolute reference frame
• Law of composition of speeds and accelerations

               - Dynamics in non-galilean reference frames