The Direct Numerical Calculation of Elliptic Functions and Integrals

1925 ◽  
Vol 12 (175) ◽  
pp. 353
Author(s):  
Nemo ◽  
L. V. King
Keyword(s):  
Numerical Calculation ◽  
Elliptic Functions ◽  
Elliptic Functions And Integrals

scholarly journals Complex variables approach to the short-axis-mode rotation of a rigid body

2018 ◽  
Vol 3 (2) ◽  
pp. 537-552 ◽  
Author(s):  
Martin Lara
Keyword(s):  
Rigid Body ◽  
Polynomial Algebra ◽  
Elliptic Functions ◽  
Complex Variables ◽  
Gravity Gradient ◽  
Integration Scheme ◽  
Short Axis ◽  
Triaxial Rigid Body ◽  
Efficient Integration ◽  
Elliptic Functions And Integrals

AbstractDecomposition of the free (triaxial) rigid body Hamiltonian into a “main problem” and a perturbation term provides an efficient integration scheme that avoids the use of elliptic functions and integrals. In the case of short-axis-mode rotation, it is shown that the use of complex variables converts the integration of the torque-free motion by perturbations into a simple exercise of polynomial algebra that can also accommodate the gravity-gradient perturbation when the rigid body rotation is close enough to the axis of maximum inertia.

scholarly journals Analytical integration of a generalized Euler-Poinsot problem: Applications

1996 ◽  
Vol 172 ◽  
pp. 249-250
Author(s):  
R. Molina ◽  
A. Vigueras
Keyword(s):  
Jacobi Equation ◽  
Elliptic Functions ◽  
Rigid Bodies ◽  
Canonical Variables ◽  
The Earth ◽  
Analytical Integration ◽  
Rotation Of The Earth ◽  
Hamilton Jacobi Equation ◽  
Elliptic Functions And Integrals

We consider a generalized Euler-Poinsot problem for a stationary gyrostat whose first two components of the gyrostatic momentum are null. The problem is formulated in the Serret-Andoyer canonical variables and analytically integrated by means of the Hamilton-Jacobi equation in terms of elliptic functions and integrals. The obtained solutions are just the same as those for rigid bodies if a specific constant is annulled. Finally, two applications are proposed: 1) to obtain the action-angle variables of this problem, and 2) to the problem of the rotation of the Earth, using a triaxial gyrostat as a model.

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