scholarly journals Noether Invariants for Nonholonomic Systems

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 641
Author(s):  
Marcela Popescu ◽  
Paul Popescu
Keyword(s):  
Mechanical Systems ◽  
Nonholonomic Systems ◽  
Nonlinear Constraints ◽  
Base Manifold ◽  
Linear And Nonlinear

The aim of this paper is to construct Noether invariants for Lagrangian non-holonomic dynamics with affine or nonlinear constraints, considered to be adapted to a foliation on the base manifold. A set of illustrative examples is given, including linear and nonlinear Appell mechanical systems.

Mechanical systems with nonlinear constraints

1997 ◽  
Vol 36 (4) ◽  
pp. 979-995 ◽  
Author(s):  
Manuel de León ◽  
Juan C. Marrero ◽  
David Martín de Diego
Keyword(s):  
Mechanical Systems ◽  
Nonlinear Constraints

NONLINEAR MODELING OF COMPLEX MECHANICAL SYSTEMS

1994 ◽  
Vol 04 (03) ◽  
pp. 521-551 ◽  
Author(s):  
MARTIN LESSER
Keyword(s):  
Nonlinear Models ◽  
Nonlinear Modeling ◽  
Mechanical Systems ◽  
Computer Software ◽  
Nonholonomic Systems ◽  
Reference List ◽  
Spacecraft Design ◽  
Vehicle Technology ◽  
Configuration Manifold ◽  
Complex Mechanical Systems

This article provides an introduction to a technique for formulating nonlinear models of mechanical systems composed of interconnected and constrained rigid body systems such as those encountered in vehicle technology, biomechanics, spacecraft design and robotics. The approach is based on an algorithm developed by Kane to treat nonholonomic systems, for example systems with rolling constraints. The algorithm is interpreted geometrically in terms of tangent vectors to the instantaneous configuration manifold embedded in the space of nonconstrained motions for the system. The level and style of the presentation is intended to be understood by scientifically literate readers with minimal knowledge in mechanics beyond the introductory level. Examples also show how computer algebra can be used to reduce the effort required for treating complex systems. An annotated reference list, which includes a discussion of computer software, is also provided.

scholarly journals Incorporating User Input Into Optimal Constraining Procedures for Survey Estimates

2013 ◽  
Vol 29 (3) ◽  
pp. 375-396 ◽  
Author(s):  
Matthew Williams ◽  
Emily Berg
Keyword(s):  
First Principles ◽  
Contingency Table ◽  
Nonlinear Constraints ◽  
Constrained Estimation ◽  
Data Set ◽  
User Input ◽  
Optimal Estimates ◽  
Linear And Nonlinear Constraints ◽  
Linear And Nonlinear ◽  
Survey Estimates

Abstract We examine the incorporation of analyst input into the constrained estimation process. In the calibration literature, there are numerous examples of estimators with “optimal” properties. We show that many of these can be derived from first principles. Furthermore, we provide mechanisms for injecting user input to create user-constrained optimal estimates. We include derivations for common deviance measures with linear and nonlinear constraints and we demonstrate these methods on a contingency table and a simulated survey data set. R code and examples are available at https://github.com/mwilli/Constrained-estimation.git.

Robust Constrained Optimization of Short- and Long-Term Net Present Value for Closed-Loop Reservoir Management

SPE Journal ◽  
2012 ◽  
Vol 17 (03) ◽  
pp. 849-864 ◽  
Author(s):  
C.. Chen ◽  
G.. Li ◽  
A.C.. C. Reynolds
Keyword(s):  
Life Cycle ◽  
Net Present Value ◽  
Production Optimization ◽  
Nonlinear Constraints ◽  
Present Value ◽  
Short Term ◽  
Linear And Nonlinear Constraints ◽  
Linear And Nonlinear ◽  
Reservoir Description

Summary In this paper, we develop an efficient algorithm for production optimization under linear and nonlinear constraints and an uncertain reservoir description. The linear and nonlinear constraints are incorporated into the objective function using the augmented Lagrangian method, and the bound constraints are enforced using a gradient-projection trust-region method. Robust long-term optimization maximizes the expected life-cycle net present value (NPV) over a set of geological models, which represent the uncertainty in reservoir description. Because the life-cycle optimal controls may be in conflict with the operator's objective of maximizing short-time production, the method is adapted to maximize the expectation of short-term NPV over the next 1 or 2 years subject to the constraint that the life-cycle NPV will not be substantially decreased. The technique is applied to synthetic reservoir problems to demonstrate its efficiency and robustness. Experiments show that the field cannot always achieve the optimal NPV using the optimal well controls obtained on the basis of a single but uncertain reservoir model, whereas the application of robust optimization reduces this risk significantly. Experimental results also show that robust sequential optimization on each short-term period is not able to achieve an expected life-cycle NPV as high as that obtained with robust long-term optimization.

scholarly journals On the Use of Linear and Nonlinear Controls for Mechanical Systems Subjected to Friction-Induced Vibration

2020 ◽  
Vol 10 (6) ◽  
pp. 2085
Author(s):  
Baptiste Chomette ◽  
Jean-Jacques Sinou
Keyword(s):  
Signal To Noise Ratio ◽  
Physical Phenomenon ◽  
Mechanical Systems ◽  
Industrial Applications ◽  
Control Vector ◽  
Controlled Systems ◽  
Control Gain ◽  
Complete Study ◽  
Linear And Nonlinear ◽  
Friction Induced Vibration

Friction-Induced Vibration and noisE (FIVE) is still a complex and nonlinear physical phenomenon which is characterized by the appearance of instabilities and self-sustained vibrations. This undesirable vibrational phenomenon is encountered in numerous industrial applications and can cause major failures for mechanical systems. One possibility to limit this vibration phenomenon due to the appearance of instabilities is to add a controller on the system. This study proposes to discuss the efficiency but also limitations of an active control design based on full linearization feedback. In order to achieve this goal, a complete study is performed on a phenomenological mechanical system subjected to mono or multi-instabilities in the presence of friction. Transient and self-excited vibrations of the uncontrolled and controlled systems are compared. More specifically, contributions of linear and nonlinear parts in the control vector for different values of friction coefficient are investigated and the influence of the control gain and sensitivity of the controller to the signal-to-noise ratio are undertaken.

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