Newtonian Dynamics PC

This course is partly intended to build upon the knowledge covered during the first semester of the first year (General Physics). With this in mind, we will cover positioning in three-dimensional space, the associated kinematics, and mechanics in non-Galilean reference frames. 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 the harmonic oscillator, and the motion of celestial bodies (Kepler’s laws).

By the end of the program, a student should be able to qualitatively predict the behavior of common mechanical systems and understand their energy behavior. The student should be able to conduct a comprehensive quantitative analysis using a simplified model of the system under study.

This course is intended for students who have already completed their first year of college. Students enrolling in this course must have a solid grasp of the following mathematical concepts: trigonometric formulas, complex numbers (real part, imaginary part, modulus, and argument), the dot product, functions of a real variable, derivatives, integrals, first-order series expansions, and differential equations.

Recommended prerequisites*: The vector product, the mixed product, and the 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.

Continuous Assessment (CA) + Final Exam. Grade = Max(0.3 × CA + 0.7 × FE)

CH I : 3D COORDINATE SYSTEMS

• An observer's reference frame and point of reference
• Different coordinate systems
• Coordinate surfaces and lines

CH II : PHYSICAL QUANTITIES

• Scalar and Vector Quantities
• Collinear and coplanar vectors, and bases for decomposition
• Construction of the local basis associated with a coordinate system
• Scalar Product and Different Expressions for 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
• Cross-Product, Elementary Volume, and Volume Calculations

CH IV : GRADIENT OPERATOR

• Gradient of a scalar field
• Completing the Form
• Circulation of a vector field
• Conservative Forces and Potential Energy

CH V : STATICS OF FLUIDS

• Scalar pressure field
• Fundamental Equation of Fluid Statics
• Archimedes' Principle

CH VI : HARMONIC OSCILLATOR

• Ideal oscillator
• Damped oscillator
• Forced oscillator

CH VII : THEOREM OF KINETIC MOMENT

• Review of Point Mechanics
• Theorem on Angular Momentum
• Central-force motion
• Celestial Mechanics: Kepler's Three Laws

CH VIII : CHANGE IN FRAMEWORKS

• Law of Position Composition
• Characterization of the motion of the relative reference frame in the absolute reference frame
• Law of the Composition of Velocities and Accelerations

               • Dynamics in non-Galilean reference frames