scholarly journals Survey of Eight Modern Methods of Hamiltonian Mechanics

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 293
Author(s):  
Alexander D. Bruno ◽  
Alexander B. Batkhin
Keyword(s):  
Hamiltonian System ◽  
Periodic Solutions ◽  
Degrees Of Freedom ◽  
Linear Method ◽  
Hamiltonian Mechanics ◽  
Nonlinear Method ◽  
New Methods ◽  
Small Parameters ◽  
The Stability ◽  
Analytic Computation

Here we describe eight new methods, arisen in the last 60 years, to study solutions of a Hamiltonian system with n degrees of freedom. The first six of them are intended for systems with small parameters or without them. The methods allow to find families of periodic solutions and families of invariant n-dimensional tori by means of analytic computation near a stationary solution, near a periodic solution and near an invariant torus, using the corresponding normal form of a Hamiltonian. Then we can continue the founded families by means of numerical computation. In a Hamiltonian system without parameters, only periodic solutions and invariant n-dimensional tori form one-parameter families. The last two methods are intended for systems with not small parameters, which do not depend on time. They allow computing sets of parameters, which guarantee the stability of some solutions for linear (method seven) and nonlinear (method eight) systems. We do not consider chaotic behaviors, but only regular ones.

scholarly journals Seismic Capacity Assessment of Unreinforced Brick Masonry Building Performed According To Eurocode

2020 ◽  
Vol 2 (1) ◽  
pp. 121-125
Author(s):  
Raul Gautam ◽  
Kshitiz Paudel
Keyword(s):  
Degrees Of Freedom ◽  
Linear Method ◽  
Brick Masonry ◽  
Masonry Building ◽  
Masonry Structures ◽  
Construction Technology ◽  
Seismic Capacity ◽  
Nonlinear Method ◽  
Modeling And Analysis ◽  
Equivalent Frame

 Brick Masonry Building with cement sand mortar is a common type of building typology in Nepal. Regardless of being one of the eldest construction technology, the behavior of masonry building is still a matter of study. The uncertainty in the behavior of masonry structures is due to material heterogeneity, complex behavior under different loading conditions and may be due to less research in this arena. Different modeling strategies are used and proposed worldwide to design and to identify the seismic performance of Masonry Building. The analysis strategy ranges from the simple linear method, equivalent frame method, static nonlinear method to dynamic nonlinear, which may be chosen according to engineering design aims and research purpose. In this attempt, authors choose two degrees of freedom 3D model of Unreinforced Brick Masonry Structures which catches both overturning and hysteresis mechanisms due to the shear response implemented by the TREMURI program with static nonlinear procedures. This verified method of modeling and analysis is applied to assess the performance of three different Unreinforced Brick Masonry buildings of the same plans with different numbers of storey.

scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

Stability of Ring-Type MEMS Gyroscopes Subjected to Stochastic Angular Speed Fluctuation

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Samuel F. Asokanthan ◽  
Soroush Arghavan ◽  
Mohamed Bognash
Keyword(s):  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Microelectromechanical Systems ◽  
Damping Ratio ◽  
Operating Conditions ◽  
System Stability ◽  
System Response ◽  
Ring Type ◽  
Mems Gyroscopes ◽  
The Stability

Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.

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