Quaternion and biquaternion methods and regular models of analytical mechanics (review)

DOI10.3103/s0025654423070051MaRDI QIDQ6544321

Publication date: 27 May 2024

Published in: Mechanics of Solids (Search for Journal in Brave)

quaternions biquaternions analytical mechanics Kustaanheimo-Stiefel variables Euler (Rodrigues-Hamilton) parameters motion geometry equations of orbital motion perturbed spatial problem of two bodies regular kinematics regularization of singularities generated by gravitational forces space flight mechanics (astrodynamics)

Mathematics Subject Classification ID

Dynamics of a rigid body and of multibody systems (70E99) Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems (70-02)

Cites Work

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Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche.
Quaternions and the perturbed Kepler problem
A special perturbation method in orbital dynamics
Quaternions for regularizing celestial mechanics: The right way
On integration of kinematic equations of a rigid body's screw-motion
On the connection among three classical mechanical problems via the hypercomplex KS-transformation
A treatise on the analytical dynamics of particles and rigid bodies with an introduction to the problem of three bodies. 3. ed.
Note sur le problème des deux corps et sur une intégration nouvelle dans le problème des trois corps.
Singular trajectories and shocks in the restricted three body problem.
The screw calculus and its applicatioin to geometry and mechanics.
Von den Bewegungen und Umlegungen. (I. u. II. Abhandlung.)
Preliminary sketch of biquaternons.
The theory of asynchronous relative motion. II: Universal and regular solutions
Alternative angle-based approach to the \(\mathcal{KS}\)-map. An interpretation through symmetry and reduction
Uniform formulation for orbit computation: the intermediate elements
The Lissajous-Kustaanheimo-Stiefel transformation
Non-averaged regularized formulations as an alternative to semi-analytical orbit propagation methods
Kustaanheimo-Stiefel transformation with an arbitrary defining vector
Analysis of optimal motion control for a material point in a central field with application of quaternions
Quaternion methods and models of regular celestial mechanics and astrodynamics
The extended Lissajous-Levi-Civita transformation
Linearization: Laplace vs. Stiefel
Perturbed spatial two-body problem: regular quaternion equations of relative motion
Kustaanheimo-Stiefel regularization and the quadrupolar conjugacy
Theory of Kepler motion: The general perturbed two body problem
Geometrical and physical outlook on the cross product of two quaternions
Concerning the regularizing KS-transformation
Perturbed Kepler problem in quaternionic form
The KS-transformation in hypercomplex form
Perturbation theory of Kepler motion based on spinor regularization.
Le mouvement Keplerien et les oscillateurs harmoniques.
Sur la régularisation du problème des trois corps.
Mémoire sur le problème des trois corps.

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