Newtonian Dynamics PC

This course is partly intended to generalize the knowledge covered in the first semester of the first year (General Physics). With this in mind, we will discuss positioning in three-dimensional space, the associated kinematics, and mechanics in a non-Galilean reference frame. This course is also intended to broaden the scope of applications covered in L1S1. In this vein, we will cover fluid statics, the dynamics and energetics of harmonic oscillators, and the motion of celestial bodies (Kepler's laws).

At the end of the course, students should be able to qualitatively predict the evolution of common mechanical systems and understand their energy behavior. They should be able to conduct a complete quantitative analysis using simplified modeling of the system under study.

This course is intended for students who have already completed their first year of university studies. Students enrolling in 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 a real variable, derivatives, primitives, limited development to order 1, and differential equations.

Recommended prerequisites*: The vector product, mixed product, and necessary concepts regarding functions of several variables, partial derivatives, and systems of differential equations will be explicitly covered in the course and are therefore not required beforehand.

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

CHAPTER I : 3D COORDINATE SYSTEMS

• Reference frame and reference point of an observer
• Different coordinate systems
• Surfaces and coordinate lines

CHAPTER II : PHYSICAL QUANTITIES

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

CHAPTER 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

CHAPTER IV : GRADIENT OPERATOR

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

CH V : FLUID STATICS

• Scalar pressure field
• Fundamental equation of fluid statics
• Archimedes' principle

CHAPTER VI : HARMONIC OSCILLATOR

• Ideal oscillator
• Damped oscillator
• Forced oscillator

CHAPTER VII : THEOREM OF KINETIC MOMENTUM

• Reminders of point mechanics
• Angular momentum theorem
• Central force movement
• Celestial Mechanics: Kepler's Three Laws

CHAPTER VIII : CHANGE OF REFERENCE FRAMEWORKS

• Position composition law
• Characterization of the motion of the relative reference frame in the absolute reference frame
• Law of composition of velocities and accelerations

               • Dynamics in non-Galilean reference frames