Lecture

Dynamics of Mechanical Systems: Kinematic Laws and Equations of Motion

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In course

ME-311: Dynamical effects in mechanical design

Ce cours poursuit la compréhension des effets cinématiques et dynamiques de systèmes mécaniques complexes et introduit les bases pour les comprendre et les modéliser. L'étudiant saura expliquer et modéliser la dynamique et choisir des modèles adéquats. ...

Description

This lecture covers the formulation of kinematic laws of motion and the coupling between forces and motion in mechanical systems. It explains how to derive the laws managing the dynamics of systems using Lagrange formulation and energy balance. The instructor demonstrates the process of determining the degree of mobility, choosing generalized coordinates, expressing kinetic and potential energies, and deriving equations of motion.

Instructor

Jürg Alexander Schiffmann

Teaching & PhD PhD Students Hendrik Dietmar Schillinger, Gabriele Iovanna, Husam Jubran, Selahittin Atilay Zervent, Harshita Ravindra Agarwal, Anupam Jena, Issam Soukhmane, Tristan Wolff Schwab, Aman Jain, Masato Omotsubo, Konstantin Andreas Jacoby, Andrii Artomov, Arnau Catala I Rams, Elize Alwash, Emanuele Pallaoro, Anna Abramishvili Past EPFL PhD Students Violette Mounier, Karim Magdi Zakaria Abdelrahman Shalash, Patrick Hubert Wagner, Markus Diehl, Philipp Kaspar Bättig, Kévin Rosset, Eliott Philippe

Official source

Ontological neighbourhood

Physics

Mechanics: Classical mechanics

Related concepts (32)

Euler–Lagrange equation

In the calculus of variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. The equations were discovered in the 1750s by Swiss mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange. Because a differentiable functional is stationary at its local extrema, the Euler–Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing or maximizing it.

Potential energy

In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. The term potential energy was introduced by the 19th-century Scottish engineer and physicist William Rankine, although it has links to the ancient Greek philosopher Aristotle's concept of potentiality. Common types of potential energy include the gravitational potential energy of an object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field.

Lagrangian mechanics

In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his 1788 work, Mécanique analytique. Lagrangian mechanics describes a mechanical system as a pair consisting of a configuration space and a smooth function within that space called a Lagrangian. For many systems, where and are the kinetic and potential energy of the system, respectively.

Kinematics

Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system.

Electric potential energy

Electric potential energy is a potential energy (measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. An object may be said to have electric potential energy by virtue of either its own electric charge or its relative position to other electrically charged objects. The term "electric potential energy" is used to describe the potential energy in systems with time-variant electric fields, while the term "electrostatic potential energy" is used to describe the potential energy in systems with time-invariant electric fields.

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