Presence Of Nonconservative Forces Research Articles

Constrained evolution of Hamiltonian phase space distributions in the presence of natural, non-conservative forces

Confidence regions for spacecraft state can be constructed in phase space which encapsulate some region where there is a likelihood for the state to reside. These regions can be treated as phase space distributions or structures. Structures, such as surfaces or volumes, are constrained to preserve specific properties as they evolve in phase space under Hamiltonian dynamics. Thus, spacecraft uncertainty is then constrained by Hamiltonian flow which can provide insight into state determination. This work examines the modified constraints in the presence of non-conservative forces which relate to both probabilistic and geometric properties of the evolving uncertainty structure. The modified constraints are then derived for a Two-Body and drag environment and are shown to be valid after comparison with alternative methods. Applying the modified constraints, the constrained evolution of the confidence region is then tied to a simple physical explanation for the changing knowledge in our spacecraft state, in the atmospheric drag environment and Poynting–Robertson drag environment.

Mechanical Energy Change in Inertial Reference Frames

The mechanical energy change of a system in an inertial frame of reference equals work done by the total nonconservative force in the same frame. This relation is covariant under the Galilean transformations from inertial frame S to S′, where S′ moves with constant velocity relative to S. In the presence of nonconservative forces, such as normal and tension forces, the mechanical energy of a system can be conserved in S and not be conserved in S′. In this paper we find useful relations between the mechanical energy changes in two inertial frames of reference.

A Nonequilibrium Extension of the Clausius Heat Theorem

We generalize the Clausius (in)equality to overdamped mesoscopic and macroscopic diffusions in the presence of nonconservative forces. In contrast to previous frameworks, we use a decomposition scheme for heat which is based on an exact variant of the Minimum Entropy Production Principle as obtained from dynamical fluctuation theory. This new extended heat theorem holds true for arbitrary driving and does not require assumptions of local or close to equilibrium. The argument remains exactly intact for diffusing fields where the fields correspond to macroscopic profiles of interacting particles under hydrodynamic fluctuations. We also show that the change of Shannon entropy is related to the antisymmetric part under a modified time-reversal of the time-integrated entropy flux.

Gyroscopic stabilization in the presence of nonconservative forces

This paper analyzes the stability of a linear autonomous nonconservative system with an even number of degrees of freedom in the presence of potential, gyroscopic, dissipative, and nonconservative positional forces. It is well known that, when applied separately, dissipative and nonconservative positional forces destroy gyroscopic stabilization [1, 3]. However, their combination can make a system asymptotically stable. It is found that the complexity of the choice of such a combination is associated with a Whitney umbrella singularity existing on the boundary of the gyroscopic stabilization domain of the nonconservative system. In this paper, an approximation to the boundary of the asymptotic stability domain near the singularity is explicitly found and an analytical estimate of the critical gyroscopic parameter is obtained. As an example, we analyze the stability of Hauger’s gyropendulum under the action of a follower torque. 1. Consider an autonomous nonconservative system of the form

Vibration of rods with a concentrated mass in the presence of non-conservative forces

Separable and non-selfadjoint boundary-value problems representing the vibration of linearly elastic unidimensional systems are considered. The elastic system is modelled as a continuous distributed-parameter system where singularities in the mass distribution function can be neatly taken into account. Specifically, extending Green's function approach, the free vibration, stability and forced vibration of fixed-free rods with a tip mass and under the action of uniformly distributed non-conservative loads have been investigated analytically.

Vibration of rods with a concentrated mass in the presence of non-conservative forces

Vibration of rods with a concentrated mass in the presence of non-conservative forces

Stability of elastic rods via Liapunov's second method

Stability of elastic rods subjected to nonconservative tangential follower forces is rigorously investigated by means of Liapunov's Second Method in the version of Movchan, Knops, and Wilkes, i.e., adapted to the specific nature of continuous systems. The result is that for such, rods internal viscous damping should have a sufficiently large magnitude in order to ensure stability. This is in agreement with, the well known fact that small damping destabilizes in the presence of nonconservative forces.