Hamiltonian mechanics | Dimensional analysis | Dynamical systems
In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. It is the outer product of direct space and reciprocal space. The concept of phase space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré, and Josiah Willard Gibbs. (Wikipedia).
Covariant Phase Space with Boundaries - Daniel Harlow
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From playlist Natural Sciences
What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:
From playlist Science Unplugged: Physics
What is a dimension? In 3D...and 2D... and 1D
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From playlist MinutePhysics
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From playlist Science Unplugged: Special Relativity
Phase space representation of billiards interpolating between a circle and a hexagon
In this simulation, I wanted to see what happens when you continuously deform the boundary of a billiard from a circle to a regular hexagon. The billiard in a circle has very regular dynamics (the technical work is "integrable"), because a given trajectory always hits the boundary with the
From playlist Particles in billiards
Ryan Thorngren - Higher Berry Phase and Diabolical Points in Phase Diagrams of Many-body Systems
The Berry phase is a well-known phenomenon in quantum mechanics with many profound implications. It describes the response of the phase of the wavefunction to the adiabatic evolution of system parameters, defining a U(1) connection on the parameter space. In many-body systems described by
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EARTH FROM SPACE: Like You've Never Seen Before
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From playlist Space Videos
Phase space representation of the billiard in an annulus
This video shows phase space representations of billiards in annular regions, obtained by moving a smaller circle inside a larger one. Phase space representations are a tool widely used by mathematicians to analyze the dynamics of mathematical billiards. This representation allows to obta
From playlist Particles in billiards
Dimensions (1 of 3: The Traditional Definition - Directions)
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From playlist Exploring Mathematics: Fractals
Geometry and Topology in Quantum Mechanics - Mathematical Properties by N. Mukunda
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From playlist Geometric Phases in Optics and Topological Matter 2020
Lecture 7 | Modern Physics: Classical Mechanics (Stanford)
Lecture 7 of Leonard Susskind's Modern Physics course concentrating on Classical Mechanics. Recorded November 26, 2007 at Stanford University. This Stanford Continuing Studies course is the first of a six-quarter sequence of classes exploring the essential theoretical foundations of mo
From playlist Course | Modern Physics: Classical Mechanics
Let's Learn Physics: Chaos in Phase Space
We have seen how Hamiltonian mechanics can be used to solve for the dynamics of physical systems. It turns out that there is quite a bit of hidden power in this formalism in that we can prove some fairly general statements about physics as a whole. We will see one of these results, known a
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Lecture 6 | Modern Physics: Statistical Mechanics
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From playlist Lecture Collection | Modern Physics: Statistical Mechanics
Ross Harder - Bragg Coherent Diffraction Imaging at the Advanced Photon Source 34-ID Beamline
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From playlist 2022 Diffractive Imaging with Phase Retrieval - - Computational Microscopy
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Phases to Phases: An invitation to Topological Phases of Many Particles by Vijay shenoy
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From playlist Geometric Phases in Optics and Topological Matter 2020
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Open Space 55: Jason Derleth, NASA's Innovative Advanced Concepts
This week I'm joined by Jason Derleth from NASA's Innovative Advanced Concepts (or NIAC). This is a special part of NASA that funds innovative ideas for new telescopes, propulsion systems and rovers. Many of the cool, science-fiction ideas I present on this channel come from research done
From playlist Open Space - Live QA with Fraser Cain and Guests