Hyperbolic Rotations of Spacetime Summary: In this class, we will review how Lorentz transformations can be reinterpreted as spacetime rotation transformations. We will start by examining rotations in the four-dimensional Minkowski space, distinguishing between purely spatial rotations and those involving spacetime axes. LEARNING OBJECTIVES: By the end of this class,...
Work and Mechanical Energy Summary: We will dedicate this series of classes to studying the relationship between work, energy, and some of its forms: kinetic and potential. From these analyses, we will calculate the stopping distance of a mobile that starts with an initial speed and travels until it stops....
Newton's Laws Summary: This class addresses Newton's laws and their role in the dynamics of bodies. It explores how mass and velocity determine linear momentum and describes the three laws: inertia, which maintains the state of motion in the absence of external forces, the relationship between force and acceleration, and...
Variational Calculus in Classical Mechanics and the Euler-Lagrange Equation Abstract:In this class, we will review the derivation of the Euler-Lagrange equation of Analytical Mechanics through the use of variational calculus techniques, and from this, we will show in detail its application in solving the Brachistochrone problem. Learning Objectives: By the...
