Engineering topics
Publications and source records attributed to Gunderson, R. W..
A general result for the controllability of linear systems using positive controls was given by Saperstone and Yorke (1971). These results are applied to systems with nearly nonnegative matrices and a theorem is developed which delineates the geometry of the reachable set.
Some results of bifurcation theory were used to study the existence of small-amplitude periodic behavior in launch vehicle dynamics, assuming that nonlinearity exists as a cubic term in the rudder response. The analysis follows closely Sattinger's (1973) approach to the theory of periodic bifurcations. The conditions under which a bifurcating branch of orbitally stable periodic solutions will exist are determined. It is shown that in more complicated cases, the conditions under which the system matrix has a pair of simple purely imaginary eigenvalues can be determined with the aid of linear stability techniques.
A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.
Two approaches are investigated for obtaining estimates on the error between approximate and exact solutions of dynamic systems. The first method is primarily useful if the system is nonlinear and of low dimension. The second requires construction of a system of v-functions but is useful for higher dimensional systems, either linear or nonlinear.
A result on differential inequalities is obtained by considering the adjoint differential equation of the variational equation of the right side of the inequality. The main theorem is proved using basic results on differentiability of solutions with respect to initial conditions. The result is then applied to the problem of determining solution behavior using comparison techniques.
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Linear comparison systems stability condition proved with Kotelianskii and Bailey theorems
Linear and nonlinear systems, and differential equations for control and stability theory
Equivalence of stability in solutions of differential equations identified with Liapunov concept
Vector differential equation, considering stability over finite interval
Transformation to phase variable canonical form
Man-machine system in control and guidance of Saturn V launch vehicle, emphasizing participation during atmospheric phase of flight profile
Feasibility of manned participation in control of large launch vehicle
Ability of pilot to stabilize flexibile launch vehicle during first stage - Saturn V launch vehicle