Newtonian dynamics PC

This course is designed in part to generalize the knowledge acquired in the first semester of the first year (General Physics). In this context, the course will deal with orientation in three-dimensional space, associated kinematics and mechanics in a non-galilean frame of reference. This course is also intended to broaden the scope of applications covered in L1S1. These include fluid statics, the dynamics and energetics of the harmonic oscillator, and the motion of celestial bodies (Kepler's laws).

At the end of the cycle, students should be able to qualitatively predict the evolution of common mechanical systems and understand their energetic behavior. They should be able to carry out a complete quantitative analysis within the framework of a simplified model of the system studied.

This course is designed for students who have already completed the first year of university education. Students taking 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 order 1 and differential equations.

Recommended prerequisites* : Vector product, mixed product and the necessary notions of 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 3D COORDINATE SYSTEMS

• Reference frame and observer's reference frame
• Different coordinate systems
• Coordinated surfaces and lines

CH II PHYSICAL QUANTITIES

• Scalar and vector quantities
• Co-linear and coplanar vectors and decomposition bases
• Construction of the local basis 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
• Drawing up the form
• Circulation of a vector field
• Conservative forces and potential energy

CH V FLUID STATICS

• Scalar pressure field
• 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
• The angular momentum theorem
• Central force movement
• Celestial mechanics: Kepler's three laws

CH VIII CHANGING REFERENCE FRAMES

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

               - Dynamics in non-galilean reference frames