The following figure employs the linearized equation and the high potential graphing equation derived above.
2.
In this way, linearized equations are derived which describe the propagation of the acoustic waves in a homogeneous, resting medium.
3.
The critical Rayleigh number can be obtained analytically for a number of different boundary conditions by doing a perturbation analysis on the linearized equations in the stable state.
4.
Second, it has been argued by Santos Silva and Tenreyro ( 2006 ) that estimating the log-linearized equation by least squares ( OLS ) can lead to significant biases.
5.
In 2007, Meijaard, et al ., published the canonical linearized equations of motion, in the " Proceedings of the Royal Society A ", along with verification by two different methods.
6.
148 . " Integrals of Linearized Differential Equations of Motion of Mechanical Systems; Part II : Linearized Equations of Motion, " J . Applied Mech ., Vol . 54, No . 3, pp . 661 667, 1987 . ( With S . Djerassi)
7.
It is possible to calculate eigenvalues, one for each of the four state variables ( lean angle, lean rate, steer angle, and steer rate ), from the linearized equations in order to analyze the normal modes and self-stability of a particular bike design.
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