Lecture

Generalized Coordinates: Constraints, Equilibria, Stability

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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 the concept of generalized coordinates in mechanics, including constraints, degrees of freedom, and equilibrium points. Examples such as simple and double pendulums are used to illustrate these concepts, emphasizing the importance of using elegant and recommended polar coordinates over complicated Cartesian coordinates for solving motion equations.

Instructor

Jean-Philippe Hogge

Teaching & PhD PhD Students Constant Philippe Panisset, Pierrick Paul Louis Giroud-Garampon Past EPFL PhD Students Sudheer Kumar Jawla, Guillaume Michel Le Bars Past EPFL PhD Students as codirector Falk Braunmüller Courses Fusion and industrial plasma technologies PHYS-632 The course provides an overview of the technologies that are essential for fusion developments and for industrial plasmaapplications, highlighting the synergies between the two fields. The aim is to provide a combined th

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.

Physics

Physics is the natural science of matter, involving the study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. A scientist who specializes in the field of physics is called a physicist. Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest.

Pendulum (mechanics)

A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity. 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 it back and forth. The mathematics of pendulums are in general quite complicated.

Elastic pendulum

In physics and mathematics, in the area of dynamical systems, an elastic pendulum (also called spring pendulum or swinging spring) is a physical system where a piece of mass is connected to a spring so that the resulting motion contains elements of both a simple pendulum and a one-dimensional spring-mass system. The system exhibits chaotic behaviour and is sensitive to initial conditions. The motion of an elastic pendulum is governed by a set of coupled ordinary differential equations.

Kater's pendulum

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