Abstract
The topic of dynamics has been somehow reshaped by computational power. The areas of computer algebra and symbolics now allow us to deal with a more involved analytical manipulation of equations. At the same time, the everyday increasing power of numerics put into our hands new tools to solve old problems. In this case, we reformulate the problem of the dynamics of a three body multibody system by using symbolic manipulation of the Newtonian equations, to produce a set of differential equations that can be solve with standard codes. This treatment should produce not only the same results as the numerical approach, but it allows us to use the analytical equations to expand the analysis into design, control and stability. The paper shows the process to build the symbolic code using Maple language, or any algebraic manipulator. The proper equations will be derived to solve for the unknowns angles {ψ,ϕ,θ}, in terms of the prescribed quantities {α(t),β(t),γ(t)t}, and initial conditions. This procedure gives a good idea about the nonlinear response of the satellite to the control parameters. The size of the equations obtained is large. However, considering the type of analysis that could be done with a set like this and the capacity of large computers, it will pay off the extra effort. The codes that could be used for further analysis would find folds, branch points, period doubling bifurcations, Hopf bifurcations, torus bifurcations, by changing the parameters of the governing equation. A large number of important applications will develop in this area in the near future.
Ekspektasi Sosial Pemuda Sasak dalam Nasyid Ya Fata Sasak Karya Hamzanwadi