Concept
Symplectic geometry
Related lectures (33)
Symmetry Property: Riemannian Connection in Geometry
Explores symmetries, Riemannian connection, vector fields, and Lie bracket in geometry.
Riemannian Hessians: Connections and SymmetryMOOC: Introduction to optimization on smooth manifolds: first order methods
Covers connections on manifolds, symmetric connections, Lie brackets, and compatibility with the metric in Riemannian geometry.
Harmonic Oscillator: Numerical Stability Analysis
Explores numerical methods for the harmonic oscillator, focusing on stability and convergence in solving oscillatory systems.
Linear Beam Dynamics
Explores particle accelerator dynamics, transfer maps, Hamiltonian equations, and phase space conservation.
Topological Polyhedron: Creating a Pavilion in TopSolid
Demonstrates creating a pavilion using a topological cube in TopSolid, emphasizing geometric accuracy and practical modeling techniques.
Canonical Transformations: Symplectic Group and Properties
Explores canonical transformations, symplectic groups, real matrices, preserved quantities, and volumes in phase space.
Geometry: Euclidean Propositions and Architectural Foundations
Explores Euclid's first proposition and its architectural implications, emphasizing the enduring relevance of classical geometric principles in contemporary architectural practice.
Non-linear dynamics: phenomenology, tools and methods
Explores Hamiltonian and Lagrangian formulations, canonical variables, Lie operators, and their applications in beam dynamics and nonlinear systems.
Continuum Mechanics: Conservation Laws, Tensor Objects, and Fluid Dynamics
Covers conservation laws, tensor objects, and fluid dynamics in Continuum Mechanics.
Canonical Transformations: Properties and Applications
Explores canonical transformations, their properties, and applications in Hamiltonian mechanics, emphasizing their role in simplifying the analysis of complex systems.