Minimum stopband attenuation of Cauer filters without elliptic functions and integrals

1993 ◽  
Vol 40 (9) ◽  
pp. 618-621 ◽  
Author(s):  
D.M. Rabrenovic ◽  
M.D. Lutovac
Keyword(s):  
Elliptic Functions ◽  
Stopband Attenuation ◽  
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.

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

Sign in / Sign up

Export Citation Format

Share Document