Search results
Results from the WOW.Com Content Network
Since the Helmholtz equation is a prototypical equation for modeling the spatial variation of classical waves, Mathieu functions can be used to describe a variety of wave phenomena. For instance, in computational electromagnetics they can be used to analyze the scattering of electromagnetic waves off elliptic cylinders, and wave propagation in ...
The Mathieu equation is a linear second-order differential equation with periodic coefficients. For q = 0, it reduces to the well-known harmonic oscillator, a being the square of the frequency. [4] The solution of the Mathieu equation is the elliptic-cylinder harmonic, known as Mathieu functions. They have long been applied on a broad scope of ...
Hill's equation is an important example in the understanding of periodic differential equations. Depending on the exact shape of f ( t ) {\displaystyle f(t)} , solutions may stay bounded for all time, or the amplitude of the oscillations in solutions may grow exponentially. [ 3 ]
Émile Mathieu was born into a family of minor civil servants. His father, Nicolas Mathieu, was a cashier at the Tax Office of the city. His mother, Amélie Antoinette Aubertin, was from Metz while her brother, Pierre Aubertin, the uncle of our mathematician, had attended the École Polytechnique, was a colonel of artillery and the director of a foundry which made cannons. Émile Mathieu was ...
Floquet theory is very important for the study of dynamical systems, such as the Mathieu equation. Floquet theory shows stability in Hill differential equation (introduced by George William Hill) approximating the motion of the moon as a harmonic oscillator in a periodic gravitational field.
Bitcoin could hit $500,000 by the end of Trump's second term, Standard Chartered estimates. The token will rise amid better investor access and lower volatility. Falling bond yields are a positive ...
The general solution of the above differential equation for a given value of a and q is a set of linearly independent Mathieu cosines and Mathieu sines, which are even and odd solutions respectively. In general, the Mathieu functions are aperiodic; however, for characteristic values of a n ( q ) , b n ( q ) {\displaystyle a_{n}(q),b_{n}(q ...
This week, explore decoded words from charred ancient scrolls, meet heroic frog daddies, see Grand Canyon-size lunar features, and more.