Abstract :
Variational equations are derived as a preliminary step in determining efficient digital integration techniques for nonlinear dynamical systems. The variational approach is applied initially to linear time-invariant systems to introduce the basic concept and then to nonlinear time-varying systems. For systems containing both linear and nonlinear parts, a combination technique which uses the exact difference equation for the linear part is developed. Higher order variational equations are also derived and compared on a simple system. Numerical approximations for solving these variational equations are discussed and illustrated for a second-order mildly nonlinear example. A significant improvement in both accuracy and execution time is realized over results obtained by the conventional fourth-order Runge–Kutta method. Finally, the new approach is discussed from the viewpoint of computational experience and special limitations for practical applications.
Keywords :
Computational accuracy versus speed, digital integration, hybrid simulation, nonlinear ordinary differential equations, numerical approximations, real-time digital simulation, state transition method, variational technique.; Computational modeling; Difference equations; Differential equations; Laboratories; Missiles; Nonlinear dynamical systems; Nonlinear equations; Nonlinear systems; Piecewise linear approximation; Time varying systems; Computational accuracy versus speed, digital integration, hybrid simulation, nonlinear ordinary differential equations, numerical approximations, real-time digital simulation, state transition method, variational technique.;
