Resonance in regular variables II: Formal solutions for central and non-central first-order resonance

1985 ◽  
Vol 35 (3) ◽  
pp. 221-234 ◽  
Author(s):  
S. Ferraz-Mello
Keyword(s):  
Order Resonance ◽  
First Order ◽  
Formal Solutions

scholarly journals Modelling Very-High-Eccentricity Asteroidal Librations with the Andoyer Hamiltonian

1999 ◽  
Vol 172 ◽  
pp. 389-390
Author(s):  
A. Simula ◽  
S. Ferraz-Mello ◽  
C. Giordano
Keyword(s):  
Explicit Form ◽  
Main Part ◽  
Order Approximation ◽  
High Eccentricity ◽  
Order Resonance ◽  
First Order ◽  
Main Effect ◽  
Realistic Description ◽  
First Order Approximation ◽  
Very High

High-eccentricity asteroidal librations are modelled using the high-eccentricity non-planar asymmetric expansion (Roig et al 1997). This second-degree expansion gives us the potential of the perturbing forces acting on a resonant asteroid in a first order resonance in explicit form, as a quadratic polynomial in the canonical non-singular variables. Secular and short periodic perturbations are introduced in the model, giving a more realistic description of the dynamics.The reducing Sessin’s transformation (Sessin, 1981; Sessin & Ferraz-Mello, 1984) is used to include the main effect of Jupiter’s ecc entricity in the main part of the Hamiltonian. It leads to an integrable first-order approximation known as the second fundamental model for resonance (Henrard & Lemaitre 1983) or Andoyer Hamiltonian (Andoyer 1903).

scholarly journals FIRST-ORDER RESONANCE OVERLAP AND THE STABILITY OF CLOSE TWO-PLANET SYSTEMS

2013 ◽  
Vol 774 (2) ◽  
pp. 129 ◽  
Author(s):  
Katherine M. Deck ◽  
Matthew Payne ◽  
Matthew J. Holman
Keyword(s):  
Order Resonance ◽  
First Order ◽  
Resonance Overlap ◽  
The Stability

Mappings for the First Order Asteroidal Resonance

1992 ◽  
Vol 152 ◽  
pp. 391-394
Author(s):  
T. J. Stuchi ◽  
W. Sessin
Keyword(s):  
Exact Solution ◽  
Periodic Function ◽  
Perturbation Technique ◽  
Simplified Model ◽  
Poincaré Mapping ◽  
Order Resonance ◽  
First Order ◽  
Poincare Mapping

We construct a two step algebraic mapping from Sessin's simplified model for the first order resonance. The orbits obtained with this mapping are compared to the ones calculated with the exact solution. We also derive a reduced Hamiltonian. A plane Poincaré mapping, using delta periodic function, is constructed and compared to the reduced Hamiltonian contour curves showing the splitting of the separatrix due to delta perturbation technique.

The Trapezoid Counterweight Method in Dynamic Balance of Symmetric Flexible Rotor

2017 ◽  
Vol 868 ◽  
pp. 201-206
Author(s):  
Han Hui ◽  
Li Na Hao ◽  
Zhang Qi ◽  
Gao Xiang
Keyword(s):  
Dynamic Balance ◽  
Reaction Force ◽  
Resonance Region ◽  
Second Order ◽  
Theoretical Research ◽  
Response Analysis ◽  
Water Pump ◽  
Flexible Rotor ◽  
Order Resonance ◽  
First Order

Steam turbine generator unit, water pump and other high speed revolution symmetric flexible rotor were regarded as research objects in this paper. According to variation characteristic of rotor shaft in rigid and flexible working mode, nine-reel high pressure water pump rotor was analyzed. The former four-order intrinsic frequency of flexible rotor was obtained by modal analysis and harmonic response analysis. The methods of reaction force response and unbalance response were been studied after first order and second order resonance region eliminating in different modes of simple harmonic exciting force. Based on above theoretical research results, trapezoid counterweight method was proposed for dynamic balance of flexible rotor. This method solved problem that rigid dynamic balance of low speed rotor was destroyed after first order and second order resonance region counter weight in dynamic balance of flexible rotor. The dynamic balancing techniques of flexible rotor could be improved the qualities of rotor and its relative products by this method, eliminating the vibration of unbalance mass of products radically.

scholarly journals Periodic Solutions for the Eccentricity and Inclination First Order Resonance

1992 ◽  
Vol 152 ◽  
pp. 231-232
Author(s):  
Marisa A. Nitto ◽  
Wagner Sessin
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Periodic Solutions ◽  
Reference System ◽  
Resonance Problem ◽  
Order Resonance ◽  
First Order ◽  
Primary Body ◽  
Different Types ◽  
The Subject

For the first order resonance, the problem of the motion of two small masses around a primary body can be of three different types: eccentricity, inclination or eccentricity-inclination. The eccentricity type resonance problem has been the subject of several works since Poincaré(1902). The inclination type resonance problem was studied by Greenberg(1973) who used a particular reference system to obtain an integrable auxiliary system. Sessin and Ferraz-Mello(1984) studied the eccentricity type resonance problem considering the eccentricities of the orbits of the two small masses. Sessin(1991) study the inclination type resonance problem for an arbitrary reference system. In this paper we will study a dynamical system that includes both types of resonance. This study is based in the models developed by Sessin and Ferraz-Mello(1984) and Sessin(1991). The resulting system of differential equation is non-integrable; thus, the families of trivial periodic solutions are studied.

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