Lecture

Dynamics of Discrete Systems

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In course

MATH-115(b): Advanced linear algebra II

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et de démontrer rigoureusement les résultats principaux du sujet. ...

Description

This lecture covers the dynamics of discrete systems, focusing on the state space, time discretization, and system evolution. It discusses deterministic systems, state transitions, and the concept of orbits in the context of Riemann varieties.

Instructor

Marc Troyanov

Expertise Differential Geometry Geometric Analysis Teaching & PhD Past EPFL PhD Students Olivier Mermoud, Khaled Gafaiti, Serguei Timochine, Stephen Ducret, Ratiba Djelid, Zahra Sinaei, Luc Genton, Adrien Giuliano Marcone, Guillaume Buro, Bruno Luiz Santos Correia Courses Advanced linear algebra II MATH-115(b) The purpose of this course is to introduce some basic notions of linear algebra and to rigorously prove the main results in the field.

Official source

Related concepts (32)

Orbit

In celestial mechanics, an orbit (also known as orbital revolution) is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory.

Deterministic system

In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system. A deterministic model will thus always produce the same output from a given starting condition or initial state. Physical laws that are described by differential equations represent deterministic systems, even though the state of the system at a given point in time may be difficult to describe explicitly.

Discrete mathematics

Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry.

Horseshoe orbit

In celestial mechanics, a horseshoe orbit is a type of co-orbital motion of a small orbiting body relative to a larger orbiting body. The osculating (instantaneous) orbital period of the smaller body remains very near that of the larger body, and if its orbit is a little more eccentric than that of the larger body, during every period it appears to trace an ellipse around a point on the larger object's orbit. However, the loop is not closed but drifts forward or backward so that the point it circles will appear to move smoothly along the larger body's orbit over a long period of time.

Orbital mechanics

Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal gravitation. Orbital mechanics is a core discipline within space-mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets.

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