
Explore the double pendulum by modeling and simulating it, using calculus of variations, with examples in Matlab and visual Python.
Derives the equations of motion for a double pendulum using calculus of variations, trigonometry, and chain-rule differentiation of the x and y coordinates and their time derivatives.
Compute the kinetic energy of masses from x dot and y dot, derive the potential energy, and form the Lagrangian T minus U to apply Euler–Lagrange to the double pendulum.
Apply the Euler-Lagrange equation to the double pendulum’s Lagrangian to derive two second-order equations for theta1 and theta2.
Convert the double pendulum's coupled second-order equations into four first-order equations using omega1, omega2, and delta theta, then solve for omega1 dot and omega2 dot, and set up MATLAB simulation.
Explore a Python-based Vpython simulation of a double pendulum, detailing L1, L2, M1, M2, gravity, angle updates, and the use of the calculus of variations and the Lagrangian method.
These videos showcase the power of Calculus of Variations. If you want to derive , code and simulate the double pendulum then this is the course you want to take.
If you like this course and would like to understand more about this fascinating subject then I have two further courses on the Calculus of Variations on Udemy.
In this course I derive the equations of motion of a double pendulum using the Calculus of Variations.
I have created this course in order to highlight how the Calculus of Variations is of fundamental importance to mathematical modelling of the physical sciences. This is a subject that is at the very heart of the physical world we see around us everyday.
The mathematics in this course is not easy but you will gain a great deal of knowledge by taking your time and just thinking about each of the equations in turn.
We will simulate the equations of motion in Matlab and in Visual Python. All the simulation files are available to you and you can run them on Matlab or Visual Python which is free to use. At the end of this course you should have a fully functioning simulation of the trajectory of a double pendulum.
This is a small part of a full suite of courses that I have available covering the area of Applied Mathematics and Computer Science. If you want to run this model of the full double pendulum on a computer that you have designed yourself from scratch then I have courses available that will let you do just that.
If you want to see how beautiful and useful mathematics is then this is the course you need to take.