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

Lecture

Dynamical Systems: Lecture 2

In course

ME-221: Dynamical systems

Provides the students with basic notions and tools for the analysis of dynamic systems. Shows them how to develop mathematical models of dynamic systems and perform analysis in time and frequency domains. ...

Description

This lecture covers the fundamentals of dynamical systems, including modeling mechanical and electrical systems, Newton's laws of motion, linear and nonlinear systems, time invariance, and the application of external forces. It also discusses the analogies between mechanical and electrical systems, Kirchhoff's law, and practical considerations in system modeling.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructor

Mahmut Selman Sakar

Official source

Related concepts (32)

Linear system

In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications. For example, the propagation medium for wireless communication systems can often be modeled by linear systems.

Linear time-invariant system

In system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance; these terms are briefly defined below. These properties apply (exactly or approximately) to many important physical systems, in which case the response y(t) of the system to an arbitrary input x(t) can be found directly using convolution: y(t) = (x ∗ h)(t) where h(t) is called the system's impulse response and ∗ represents convolution (not to be confused with multiplication).

Newton's laws of motion

Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force. When a body is acted upon by a force, the time rate of change of its momentum equals the force. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.

Newton's law of universal gravitation

Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The publication of the law has become known as the "first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors.

Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured.

Related lectures (39)

SISO Polynomial Controllers: Sylvester Matrix, Internal Model Principle

Covers the design of SISO polynomial controllers using concepts such as the Sylvester matrix and model matching.

Particle Interactions: Forces and Newton's Laws

Explores particle interactions, forces, Newton's laws, and the center of mass in systems.

Introduction to General Physics

Covers the fundamental laws of physics, electromagnetism, and the crisis of classical physics, exploring topics like the black body spectrum and atomic models.

Networked Control Systems: Fundamentals and Stability Analysis

Covers the fundamentals and stability analysis of Networked Control Systems, including software installation, dynamical systems, equilibrium states, and stability testing.

Analytical Mechanics: Newton's Three Laws