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162 views · 10 months ago ...more. Swati Theng Mathematics. 9.39K. Subscribe. 5. Share. Save. Report. Comments. thumbnail-image.
YouTube-Swati Theng Mathematics
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YouTube-AccPhys
Proof of Liouville's Theorem
Motion in the phase space
Phase space projection
Definition of space density
Phase space density
Theorem Statement
Subtraction of flowing in and flowing out
Change in rate of flow
Hamilton's equations
Conclusion
This is a corrected re-upload of a video from a couple of weeks ago. The original version contained one too many shortcut that I really ...
YouTube-Mathologer
Introduction
What are transcendental numbers?
Truncations of Liouville's number
Approximating polynomials
Explanation of Liouville's number
Problems with higher truncations
Polynomials with positive integer coefficients
Integer addition to a transcendental number
In this video I explain basics on moment maps and toric actions. I also give a conceptual proof of Arnold-Liouville theorem (feat.
YouTube-Eva Miranda
Adjoint Mapping
The Adjoint Representation
Proof of Arnold
Uniformization of Periods
This video covers Liouville's Theorem for conservative, natural systems ("natural" referring to systems for which H=T+U) whose Hamiltonians ...
YouTube-Caitlyn Johnson
What is Phase Space?
Phase space for one dimensional system
Example
Linear systems
Phase portrait of a simple pendulum
Hamiltonian Mechanics
Hamiltonian equations of motion
Divergence Theorem
Examining the integrand
The idea of this animation is to give an example of Liouville's theorem in phase space. The Hamiltonian is sin(p) + sin(x).
YouTube-North Van Physics Group