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Biryukov Equation
In the study of dynamical systems, the Biryukov equation (or Biryukov oscillator), named after Vadim Biryukov (1946), is a non-linear second-order differential equation used to model damped oscillators. The equation is given by \frac+f(y)\frac+y=0, \qquad\qquad (1) where is a piecewise constant function which is positive, except for small as \begin & f(y) = \begin -F, & , y, \le Y_0; \\ ptF, & , y, >Y_0. \end \\ pt& F = \text > 0, \quad Y_0 = \text > 0. \end Eq. (1) is a special case of the Lienard equation; it describes the auto-oscillations. Solution (1) at a separate time intervals when f(y) is constant is given by y_k(t) = A_\exp(s_t) + A_\exp(s_t) \qquad\qquad (2) where denotes the exponential function. Here s_k = \begin \displaystyle \frac\mp\sqrt, & , y, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sine Oscillations
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle \theta, the sine and cosine functions are denoted simply as \sin \theta and \cos \theta. More generally, the definitions of sine and cosine can be extended to any real value in terms of the lengths of certain line segments in a unit circle. More modern definitions express the sine and cosine as infinite series, or as the solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers. The sine and cosine functions are commonly used to model periodic phenomena such as sound and lig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
