SearcharxivSearch

arXiv · 2409.12310

On the Dynamics of a Nutation Ring Damper

Abstract

Nutation triggered by external disturbances is an undesirable phenomenon for a spinning satellite. Passive decay in nutation angle must be achieved in such cases and benefits missions involving spin-stabilized satellites or mass-constrained satellites like CubeSats. Motivated by previous work of other authors, the dynamics of a general nutating satellite with an attached ring containing a viscous fluid is analyzed in a theoretical mechanics framework. The fluid in the ring is modeled as a rigid point mass and is then extended to a distributed rigid slug. The nonlinear equations of motion of the system, under the assumption of zero external torques, are studied in a body-fixed frame. Equilibrium points and system trajectories are studied on the angular momentum sphere. The settling time of the dynamical system after an initial disturbance is investigated. The energy dissipation is modeled using an approximate drag coefficient. Fluid dynamic effects are further examined through CFD simulations in the Navier-Stokes setting using the open-source software package ANSYS Fluent. Applications of the analysis and simulations to CubeSats are discussed.

Explore related subjects

Keep this discovery

BibTeXRIS

Adrian Luna, Banavara N. Shashikanth. 2024-09-18. On the Dynamics of a Nutation Ring Damper. https://arxiv.org/abs/2409.12310

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Admissible Fourier Lengths, KAM Reducibility, and Spectral Applications

We develop a perturbative KAM reducibility theory for one-frequency $\mathrm{SL}(2,\mathbb{R})$ cocycles based on an admissible Fourier length $\ell$. The regularity relevant to the iteration is measured by positive adapted Fourier width rather than ordinary smoothness in the Euclidean length $|n|$. The same length governs Fourier decay, truncation and resonance scales, and the arithmetic condition controlling the small divisors. This framework contains the classical analytic and Gevrey settings, while non-monotone choices of $\ell$ allow classical nowhere differentiable Weierstrass-type perturbations and continuous perturbations outside every positive H\"older class. As spectral applications, we obtain purely absolutely continuous spectrum for every phase and $1/2$-H\"older continuity of the integrated density of states for the associated quasiperiodic Schr\"odinger operators. The Aubry dual has pure point spectrum for Lebesgue almost every dual phase, with eigenfunctions exponentially localized in the metric induced by $\ell$. We also construct nowhere differentiable quasiperiodic potentials with purely absolutely continuous Cantor spectrum.

math.DS

Dynamics inside the attracting basins of some skew products

Polynomial skew products in $\mathbb{C}^2$ are maps of the form $F(z,w)=(P(z),Q(z,w))$, where $P$ and $Q$ are polynomials. Their local dynamics have been widely investigated. In this paper, we study the global dynamics inside Fatou components of some skew products. We consider all the inverse images in a Fatou component of a given point and use the Kobayashi metric to measure the distance between points. In the cases we consider, there are always arbitrarily large Kobayashi balls in the complement of these inverse sets.

math.DS

Ergodicity of dynamical systems without uniqueness of orbits

Recently, there has been considerable interest in the study of non-deterministic dynamical systems. To analyze the chaotic behavior of such systems from a measure-theoretic viewpoint, it is desirable to consider ergodicity. However, the classical definition of ergodicity involves invariant sets, whose definition is not unique for non-deterministic dynamical systems. Thus, we are led to the question of which invariance yields an interesting definition of ergodicity. Here, we propose a definition based on the strong backward invariance and show that analogs of classical results hold. We also consider implications of the Birkhoff ergodic theorem for systems without uniqueness of orbits.

math.DS