Some applications of quasi-velocities in optimal control

In this paper we study optimal control problems for nonholonomic systems defined on Lie algebroids by using quasi-velocities. We consider both kinematic, i.e. systems whose cost functional depends only on position and velocities, and dynamic optimal control problems, i.e. systems whose cost functional depends also on accelerations. The formulation of the problem directly at the level of Lie algebroids turns out to be the correct framework to explain in detail similar results appeared recently (Maruskin and Bloch, 2007). We also provide several examples to illustrate our construction.Comment: Revtex 4.1, 20 pages. To appear in Int. J. Geom. Meth. Modern Physic

Dynamic Limits on Planar Libration-Orbit Coupling Around an Oblate Primary

This paper explores the dynamic properties of the planar system of an ellipsoidal satellite in an equatorial orbit about an oblate primary. In particular, we investigate the conditions for which the satellite is bound in librational motion or when the satellite will circulate with respect to the primary. We find the existence of stable equilibrium points about which the satellite can librate, and explore both the linearized and non-linear dynamics around these points. Absolute bounds are placed on the phase space of the libration-orbit coupling through the use of zero-velocity curves that exist in the system. These zero-velocity curves are used to derive a sufficient condition for when the satellite's libration is bound to less than 90 degrees. When this condition is not satisfied so that circulation of the satellite is possible, the initial conditions at zero libration angle are determined which lead to circulation of the satellite. Exact analytical conditions for circulation and the maximum libration angle are derived for the case of a small satellite in orbits of any eccentricity.Comment: Submitted to Celestial Mechanics and Dynamical Astronom

Inspiration and the promotion of well-being: Tests of causality and mediation

The influence of inspiration on well-being was examined in 4 studies. In Study 1, experimental manipulation of exposure to extraordinary competence increased positive affect, and inspiration accounted for this effect. In Study 2, trait inspiration predicted an increase in positive hedonic and eudaimonic well-being variables (positive affect, life satisfaction, vitality, and self-actualization) across a 3-month period, even when the Big 5 traits, initial levels of all well-being variables, and social desirability biases were controlled. In Study 3, both trait inspiration and personal goals inspiration predicted increases in positive well-being variables across a 3-month period. In contrast, well-being did not predict longitudinal change in inspiration. Study 4, a diary study, extended the relation between inspiration and well-being to the within-person level of analysis. For given individuals, variations in inspiration across mornings predicted variations in evening levels of positive well-being variables. These effects were mediated by purpose in life and gratitude. These studies provide converging evidence that inspiration enhances well-being and document 2 parallel mediating processes