Complex variable methods for linearized Euler rigid body rotation equations
The determination of analytical solutions is a vital step in understanding the different physical systems and building confidence in the numerical methods that are required for more complex models. In the present work, analytical solutions are derived for axisymmetric and near-axisymmetric rigid bod...
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| Vydáno v: | Acta astronautica Ročník 170; s. 454 - 465 |
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01.05.2020
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| ISSN: | 0094-5765, 1879-2030 |
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| Abstract | The determination of analytical solutions is a vital step in understanding the different physical systems and building confidence in the numerical methods that are required for more complex models. In the present work, analytical solutions are derived for axisymmetric and near-axisymmetric rigid body problems. The formulation proposed is based on a complex variable which characterizes all the different kinds of problems in similar terms. The described methodology is introduced for simple cases and, progressively, extended to other advanced problems such as random perturbations. As an application, this complex variable formulation can be used to characterize the asteroid’ motions, showing a dependence between their inertia coefficients and their rotational velocities when the asteroid is perturbed from its relaxed state. A Montecarlo experiment is done in order to determine how well the inertia ratios of the asteroid can be estimated knowing only information about its angular velocities.
•Analytical solutions are derived for axisymmetric and near-axisymmetric rigid body problems.•The formulation proposed is based on a complex variable which characterizes all the different problems in similar terms.•A Montecarlo experiment, using data from real asteroids, is done to determine how well the inertia ratios can be estimated.. |
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| AbstractList | The determination of analytical solutions is a vital step in understanding the different physical systems and building confidence in the numerical methods that are required for more complex models. In the present work, analytical solutions are derived for axisymmetric and near-axisymmetric rigid body problems. The formulation proposed is based on a complex variable which characterizes all the different kinds of problems in similar terms. The described methodology is introduced for simple cases and, progressively, extended to other advanced problems such as random perturbations. As an application, this complex variable formulation can be used to characterize the asteroid’ motions, showing a dependence between their inertia coefficients and their rotational velocities when the asteroid is perturbed from its relaxed state. A Montecarlo experiment is done in order to determine how well the inertia ratios of the asteroid can be estimated knowing only information about its angular velocities.
•Analytical solutions are derived for axisymmetric and near-axisymmetric rigid body problems.•The formulation proposed is based on a complex variable which characterizes all the different problems in similar terms.•A Montecarlo experiment, using data from real asteroids, is done to determine how well the inertia ratios can be estimated.. The determination of analytical solutions is a vital step in understanding the different physical systems and building confidence in the numerical methods that are required for more complex models. In the present work, analytical solutions are derived for axisymmetric and near-axisymmetric rigid body problems. The formulation proposed is based on a complex variable which characterizes all the different kinds of problems in similar terms. The described methodology is introduced for simple cases and, progressively, extended to other advanced problems such as random perturbations. As an application, this complex variable formulation can be used to characterize the asteroid' motions, showing a dependence between their inertia coefficients and their rotational velocities when the asteroid is perturbed from its relaxed state. A Montecarlo experiment is done in order to determine how well the inertia ratios of the asteroid can be estimated knowing only information about its angular velocities. |
| Author | Chen, Huan Cubas, Javier Sanz-Andrés, Ángel García-Gutiérrez, Adrián |
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| Cites_doi | 10.1016/j.asr.2014.10.034 10.1016/j.actaastro.2019.05.011 10.1016/j.actaastro.2008.12.015 10.1115/1.2755110 10.1007/BF00051695 10.1115/1.2901010 10.3847/1538-4357/aa8ee4 10.2514/1.62695 10.1115/1.2787190 10.1006/icar.2000.6485 10.1051/0004-6361/200912693 10.1016/j.actaastro.2018.05.023 10.1115/1.2901011 10.2514/1.12272 10.1016/j.actaastro.2017.07.043 10.1093/mnras/stx2328 10.1038/nature01948 |
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