Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

General Physics: Mechanics for SIE and GC

In course

PHYS-101(a): General physics : mechanics

Le but du cours de physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de prévoir quantitativement les conséquences de ces phénomène ...

Description

This lecture covers topics related to constraints, equilibrium points, and stability in mechanics. It discusses generalized coordinates, degrees of freedom, constraints, and stability analysis using examples like simple and double pendulums. The instructor explains the concept of stability of equilibrium points and provides analogies with a ball on different surfaces to illustrate stable and unstable equilibriums.

Instructor

Jean-Philippe Hogge

Official source

Ontological neighbourhood

Physics

Mechanics: Classical mechanics

Related concepts (32)

Pendulum

A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period.

Stability theory

In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.

Mechanical equilibrium

In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero. In addition to defining mechanical equilibrium in terms of force, there are many alternative definitions for mechanical equilibrium which are all mathematically equivalent. In terms of momentum, a system is in equilibrium if the momentum of its parts is all constant.

Equilibrium point

In mathematics, specifically in differential equations, an equilibrium point is a constant solution to a differential equation. The point is an equilibrium point for the differential equation if for all . Similarly, the point is an equilibrium point (or fixed point) for the difference equation if for . Equilibria can be classified by looking at the signs of the eigenvalues of the linearization of the equations about the equilibria.

Classical mechanics

Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility). The "classical" in "classical mechanics" does not refer classical antiquity, as it might in, say, classical architecture.

Related lectures (48)

Mechanics: Equilibrium Points and Stability

Explores equilibrium points and stability in mechanical systems, analyzing how systems return to or move away from their positions after disturbances.

Generalized Coordinates: Constraints, Equilibria, Stability

Covers generalized coordinates, constraints, degrees of freedom, and equilibrium points in mechanics.

Equilibrium Points and Stability

Explores equilibrium points and stability in mechanical systems with multiple degrees of freedom.

Mechanics: Geometric Constraints and Equilibrium Points

Explores generalized coordinates, constraints, equilibrium points, and stability in mechanics using elegant polar coordinates.

Simple Pendulum: Constraints and Equations of Motion