Stability by KAM confinement of certain wild, nongeneric relative equilibria of underwater vehicles with coincident centers of mass and bouyancy

Purely rotational relative equilibria of an ellipsoidal underwater vehicle occur at nongeneric momentum where the symplectic reduced spaces change dimension. The stability these relative equilibria under momentum changing perturbations is not accessible by Lyapunov functions obtained from energy and momentum. A blow-up construction transforms the stability problem to the analysis symmetry-breaking perturbations of Hamiltonian relative equilibria. As such, the stability follows by KAM theory rather than energy-momentum confinement.Comment: 18 pages, 3 figure

Multisymplectic geometry, variational integrators, and nonlinear PDEs

This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental geometric structures as well as their preservation along solutions can be obtained directly from the variational principle. In particular, we prove that a unique multisymplectic structure is obtained by taking the derivative of an action function, and use this structure to prove covariant generalizations of conservation of symplecticity and Noether's theorem. Natural discretization schemes for PDEs, which have these important preservation properties, then follow by choosing a discrete action functional. In the case of mechanics, we recover the variational symplectic integrators of Veselov type, while for PDEs we obtain covariant spacetime integrators which conserve the corresponding discrete multisymplectic form as well as the discrete momentum mappings corresponding to symmetries. We show that the usual notion of symplecticity along an infinite-dimensional space of fields can be naturally obtained by making a spacetime split. All of the aspects of our method are demonstrated with a nonlinear sine-Gordon equation, including computational results and a comparison with other discretization schemes.Comment: LaTeX2E, 52 pages, 11 figures, to appear in Comm. Math. Phy

Least-cost number, size, and location of turkey-processing plants in Minnesota, Iowa, and Wisconsin

In the last few years, various reports have dealt with costs of operation of turkey-processing plants. Through these reports and through their own experiences, processing plant managers are well aware of the existence of economies of large-scale operation and the reduction in costs possible from operating at or near capacity. Although the significance of economies of large-scale operation for the individual plant manager is well understood, the significance of these economies for an entire marketing system or for an entire turkey-production region has not been systematically investigated.https://lib.dr.iastate.edu/specialreports/1060/thumbnail.jp

Applications of flight control system methods to an advanced combat rotorcraft

Advanced flight control system design, analysis, and testing methodologies developed at the Ames Research Center are applied in an analytical and flight test evaluation of the Advanced Digital Optical Control System (ADOCS) demonstrator. The primary objectives are to describe the knowledge gained about the implications of digital flight control system design for rotorcraft, and to illustrate the analysis of the resulting handling-qualities in the context of the proposed new handling-qualities specification for rotorcraft. Topics covered in-depth are digital flight control design and analysis methods, flight testing techniques, ADOCS handling-qualities evaluation results, and correlation of flight test results with analytical models and the proposed handling-qualities specification. The evaluation of the ADOCS demonstrator indicates desirable response characteristics based on equivalent damping and frequency, but undersirably large effective time-delays (exceeding 240 m sec in all axes). Piloted handling-qualities are found to be desirable or adequate for all low, medium, and high pilot gain tasks; but handling-qualities are inadequate for ultra-high gain tasks such as slope and running landings

Geometric discrete analogues of tangent bundles and constrained Lagrangian systems

Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical integrators. The phase space of such variational discretizations is often the set of configuration pairs, analogously corresponding to initial and terminal points of a tangent vectors. We develop alternative discrete analogues of tangent bundles, by extending tangent vectors to finite curve segments, one curve segment for each tangent vector. Towards flexible, high order numerical integrators, we use these discrete tangent bundles as phase spaces for discretizations of the variational principles of Lagrangian systems, up to the generality of nonholonomic mechanical systems with nonlinear constraints. We obtain a self-contained and transparent development, where regularity, equations of motion, symmetry and momentum, and structure preservation, all have natural expressions.Comment: Typos corrected. New abstract. Diagrams added. Some additional information and a conclusions section adde