Differential equations | Dynamical systems
Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic linear differential equations of the form with a piecewise continuous periodic function with period and defines the state of the stability of solutions. The main theorem of Floquet theory, Floquet's theorem, due to Gaston Floquet, gives a canonical form for each fundamental matrix solution of this common linear system. It gives a coordinate change with that transforms the periodic system to a traditional linear system with constant, real coefficients. When applied to physical systems with periodic potentials, such as crystals in condensed matter physics, the result is known as Bloch's theorem. Note that the solutions of the linear differential equation form a vector space. A matrix is called a fundamental matrix solution if all columns are linearly independent solutions. A matrix is called a principal fundamental matrix solution if all columns are linearly independent solutions and there exists such that is the identity. A principal fundamental matrix can be constructed from a fundamental matrix using . The solution of the linear differential equation with the initial condition is where is any fundamental matrix solution. (Wikipedia).
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From playlist Science Unplugged: String Theory
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://twitter.com/worldscienceu
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