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Mathieu function. In mathematics, Mathieu functions, sometimes called angular Mathieu functions, are solutions of Mathieu's differential equation. where a, q are real -valued parameters. Since we may add π/2 to x to change the sign of q, it is a usual convention to set q ≥ 0.
Inverted pendulum. Balancing cart, a simple robotics system circa 1976. The cart contains a servo system that monitors the angle of the rod and moves the cart back and forth to keep it upright. An inverted pendulum is a pendulum that has its center of mass above its pivot point. It is unstable and falls over without additional help.
The Nyquist stability criterion is a graphical technique that determines the stability of a dynamical system, such as a feedback control system. It is based on the argument principle and the Nyquist plot of the open-loop transfer function of the system. It can be applied to systems that are not defined by rational functions, such as systems ...
Van der Pol oscillator. In the study of dynamical systems, the van der Pol oscillator (named for Dutch physicist Balthasar van der Pol) is a non- conservative, oscillating system with non-linear damping. It evolves in time according to the second-order differential equation where x is the position coordinate —which is a function of the time t ...
The Poincaré–Lindstedt method allows for the creation of an approximation that is accurate for all time, as follows. In addition to expressing the solution itself as an asymptotic series, form another series with which to scale time t: where. We have the leading order ω0 = 1, because when , the equation has solution .
The polyhedral model (also called the polytope method) is a mathematical framework for programs that perform large numbers of operations -- too large to be explicitly enumerated -- thereby requiring a compact representation. Nested loop programs are the typical, but not the only example, and the most common use of the model is for loop nest ...
When looking at sustained freedom from pain, researchers found that eletriptan and ibuprofen were the most effective. Researchers concluded that eletriptan, rizatriptan, sumatriptan, and ...
In the social sciences, triangulation refers to the application and combination of several research methods in the study of the same phenomenon. [1] By combining multiple observers, theories, methods, and empirical materials, researchers hope to overcome the weakness or intrinsic biases and the problems that come from single method, single-observer, and single-theory studies.