## Stability Analysis

Solving the equation of motion, one can compute s, s, / and / for the next time step, starting from the steady state position. The equations of motion are written as

The dimensionless forms of Eqs. 13.53 and 13.54 are

■■ • F/ Ms/ + 2M s / — ^ + sin / = 0 (13.56)

Wa where M = MCx2/LDps and Wa = WaC2/gmR3L. Equations 13.55 and 13.56 are second-order differential equations in s and /. These are solved by using a fourth-order Runge-Kutta method for constant values of M, Fr and F/. The integration scheme gives the eccentricity ratio, attitude angle and their derivatives. These are used in the solution of the Reynolds equation for the next time step to obtain the pressure distribution and hence the force components. The force components are then used in the solution of the equations of motion. The procedure of solving the Reynolds equation and the equations of motion is repeated until a sufficient number of £ and / values are obtained so that a trajectory can be drawn. The nature of the trajectory helps in determining the status of the system.

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