From the course: Complete Guide to Differential Equations Foundations for Data Science

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Hamiltonian systems

Hamiltonian systems

From the course: Complete Guide to Differential Equations Foundations for Data Science

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Hamiltonian systems

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- [Instructor] Let's continue exploring different types of non-linear systems of differential equations. In this video, you will focus on exploring Hamiltonian systems. Let's get started. A Hamiltonian system is a special class of dynamical systems that conserve a quantity such as energy and exhibit structured phase-space behavior. These systems frequently arise in practical applications such as physics, mechanics, and engineering. Let's look at how a Hamiltonian system is formatted. Here you have the system dx dt equals partial capital H over partial y and dy dt equals negative partial capital H over partial x. In the system you have your Hamiltonian function represented by capital H of x, y and then your system state variables x and y, which can represent quantities such as position and momentum. Note that the system does contain partial derivatives in it, but for now you can treat them like normal derivatives to make the system easier to interpret. Let's dive deeper into the…

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