May 1, 2024
3 minute read
Euler Equations, also referred to as Euler-Lagrange equations, are sets of partial differential equations (PDEs) in the calculus of variations that describe the motion of systems subject to constraints. They find a wide range of applications in physics, engineering, and mathematics.
Key Concepts
Euler Equations are derived from the principle of least action, which states that physical systems tend to follow the path that minimizes the action over time. The action is a functional of the trajectory of the system and is defined as the integral of the difference between the kinetic and potential energy of the system.
By minimizing the action with respect to variations in the trajectory, one obtains a set of partial differential equations known as Euler Equations. These equations provide necessary conditions for the trajectory of a system to be an extremum of the action functional.
Applications
Euler Equations have a wide range of applications in various fields:
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Reading list
We've selected 13 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Euler Equations.
Provides a comprehensive overview of Euler equations in plasma physics. It valuable resource for researchers who are working in this area.
Monograph on the Euler equations in geophysical fluid dynamics.
This introductory textbook provides a clear and concise overview of Euler equations, with a focus on their applications in fluid mechanics, solid mechanics, and other areas. It valuable resource for students and researchers who are new to the subject.
Provides a comprehensive overview of Euler equations for incompressible fluids. It valuable resource for researchers who are working in this area.
Provides a comprehensive overview of Euler equations in geophysical fluid dynamics. It valuable resource for researchers who are working in this area.
Provides a comprehensive overview of Euler equations for rotating fluids. It valuable resource for researchers who are working in this area.
Provides a comprehensive overview of Euler equations in elasticity and plasticity. It valuable resource for researchers who are working in this area.
Provides a comprehensive overview of Euler equations in astrophysics. It valuable resource for researchers who are working in this area.
This textbook provides a practical introduction to partial differential equations, with a focus on applications in engineering and science. It includes a chapter on Euler equations.
Provides a clear and concise overview of Euler equations in fluid mechanics. It valuable resource for students and researchers who are new to the subject.
This textbook provides a clear and concise overview of partial differential equations, including Euler equations. It valuable resource for students and researchers who are new to the subject.
Tutorial on the Euler equations, written for graduate students in mathematics and physics.
Provides a historical and mathematical exploration of Euler's polyhedron formula, which is related to Euler equations. It valuable resource for students and researchers who are interested in the history of mathematics.
For more information about how these books relate to this course, visit:
OpenCourser.com/topic/72hbal/euler
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