LitArk » Books » Home and family

Brogliato - Nonsmooth Mechanics : Models, Dynamics and Control

Here you can read online Brogliato - Nonsmooth Mechanics : Models, Dynamics and Control full text of the book (entire story) in english for free. Download pdf and epub, get meaning, cover and reviews about this ebook. City: Cham, year: 2016, publisher: Imprint, Springer, Springer International Publishing, genre: Home and family. Description of the work, (preface) as well as reviews are available. Best literature library LitArk.com created for fans of good reading and offers a wide selection of genres:

Romance novel Science fiction Adventure Detective Science History Home and family Prose Art Politics Computer Non-fiction Religion Business Children Humor

Choose a favorite category and find really read worthwhile books. Enjoy immersion in the world of imagination, feel the emotions of the characters or learn something new for yourself, make an fascinating discovery.

Book:
Nonsmooth Mechanics : Models, Dynamics and Control
Author:
Brogliato / Bernard
Publisher:
Imprint, Springer, Springer International Publishing
Genre:
Books / Home and family
Year:
2016
City:
Cham
Rating:
5 / 5
Favourites:
Add to favourites
Your mark:
- 100
- 1
- 2
- 3
- 4
- 5

Description
Author's other books
Similar books

Nonsmooth Mechanics : Models, Dynamics and Control: summary, description and annotation

We offer to read an annotation, description, summary or preface (depends on what the author of the book "Nonsmooth Mechanics : Models, Dynamics and Control" wrote himself). If you haven't found the necessary information about the book — write in the comments, we will try to find it.

Now in its third edition, this standard reference is a comprehensive treatment of nonsmooth mechanical systems refocused to give more prominence to control and modelling. It covers Lagrangian and Newton-Euler systems, detailing mathematical tools such as convex analysis and complementarity theory. The ways in which nonsmooth mechanics influence and are influenced by well-posedness analysis, numerical analysis and simulation, modelling and control are explained. Contact/impact laws, stability theory and trajectory-tracking control are given in-depth exposition connected by a framework formed from complementarity systems and measure-differential inclusions. Links are established with electrical circuits with set-valued nonsmooth elements and with other nonsmooth dynamical systems like impulsive and piecewise linear systems. Nonsmooth Mechanics (third edition) has been substantially rewritten, edited and updated to account for the significant body of results that have emerged in the twenty-first century--including developments in: the existence and uniqueness of solutions; impact models; extension of the Lagrange-Dirichlet theorem and trajectory tracking; and well-posedness of contact complementarity problems with and without friction. With its improved bibliography of over 1,300 references and wide-ranging coverage, Nonsmooth Mechanics (third edition) is sure to be an invaluable resource for researchers and postgraduates studying the control of mechanical systems, robotics, granular matter and relevant fields of applied mathematics. The books two best features, in my view are its detailed survey of the literature ... and its detailed presentation of many examples illustrating both the techniques and their limitations ... For readers interested in the field, this book will serve as an excellent introductory survey. Andrew Lewis in Automatica It is written with clarity, contains the latest research results in the area of impact problems for rigid bodies and is recommended for both applied mathematicians and engineers. Panagiotis D. Panagiotopoulos in Mathematical Reviews The presentation is excellent in combining rigorous mathematics with a great number of examples ... allowing the reader to understand the basic concepts. Hans Troger in Mathematical Abstracts. Read more...

Brogliato: author's other books

Who wrote Nonsmooth Mechanics : Models, Dynamics and Control? Find out the surname, the name of the author of the book and a list of all author's works by series.

Nonsmooth Mechanics : Models, Dynamics and Control — read online for free the complete book (whole text) full work

Below is the text of the book, divided by pages. System saving the place of the last page read, allows you to conveniently read the book "Nonsmooth Mechanics : Models, Dynamics and Control" online for free, without having to search again every time where you left off. Put a bookmark, and you can go to the page where you finished reading at any time.

Light

Font size:

↓

↑

Reset

Interval:

↓

↑

Bookmark:

Make

Springer International Publishing Switzerland 2016

Bernard Brogliato Nonsmooth Mechanics Communications and Control Engineering 10.1007/978-3-319-28664-8_1

1. Impulsive Dynamics and Measure Differential Equations

Bernard Brogliato 1

(1)

INRIA Rhne-Alpes, Saint-Ismier, France

Bernard Brogliato

Email:

This chapter is devoted to introducing the mathematical basis on which various evolution problems involving impulsive terms rely. Impulsive forces in mechanics are first presented disregarding what they may be produced by. It is shown on simple examples why impulsive mechanics involves only measures (Dirac functions), and no distribution of higher degree (derivatives of the Dirac function). Various classes of measure differential equations (MDEs), or impulsive systems, are introduced. Then unilaterally constrained dynamical systems are presented, and the differences with the foregoing MDEs are discussed. Variable changes that allow one to transform MDEs into Carathodory ordinary differential equations (ODEs) or unilaterally constrained mechanical systems into Filippovs differential inclusions, are described in the last section.

1.1 Impulsive Forces

Let us introduce the impacts as purely exogenous actions on a mechanical system, without considering the way by which they may be produced. In other words, we consider impulsive forces (which we may name also exogenous impacts or external percussions). Simply speaking, an impact between two bodies (not necessarily rigid) is a phenomenon of very short duration that implies a sudden change in the bodies dynamics (fast velocity variation). Impacts are treated usually as very large forces acting during an infinitely short time, i.e., if

represents the collision duration and Nonsmooth Mechanics Models Dynamics and Control - image 2

represents the force during the collision ( Nonsmooth Mechanics Models Dynamics and Control - image 3

may be viewed as a time function whose support is Nonsmooth Mechanics Models Dynamics and Control - image 4

, i.e.,

is zero outside K ), then the force impulse due to the impact at time is 11 In order for the right-hand side of - photo 6

due to the impact at time is 11 In order for the right-hand side of but this is the only - photo 7

is:

11 In order for the right-hand side of but this is the only formulation - photo 8

(1.1)

In order for the right-hand side of (), but this is the only formulation of such a phenomenon that is mathematically correct: Analogy between mathematical and physical distributions has not to be shown: mathematical distributions provide a correct mathematical definition of distributions encountered in physics , [1081, Chap. 1, p. 84].

One of the main consequences of such an approach is that the impulsive forces imply a discontinuity in the velocity while positions remain continuous. This can be understood from simple examples.

Fig. 1.1

Mass submitted to an impulsive force

Example 1.1

Assume that a mass m moving on a line, with gravity center coordinate x (the system is depicted in Fig. ), is submitted to an impulsive force of magnitude Nonsmooth Mechanics Models Dynamics and Control - image 10

Nonsmooth Mechanics Models Dynamics and Control - image 10

at the instant Nonsmooth Mechanics Models Dynamics and Control - image 11

. The dynamical equation is given by:

Nonsmooth Mechanics Models Dynamics and Control - image 12

(1.2)

which is to be understood as an equality of distributions. Assume now that x and Nonsmooth Mechanics Models Dynamics and Control - image 13

possess (possibly zero) respective jumps Nonsmooth Mechanics Models Dynamics and Control - image 14

and

Nonsmooth Mechanics Models Dynamics and Control - image 15

Nonsmooth Mechanics Models Dynamics and Control - image 16

, where

Nonsmooth Mechanics Models Dynamics and Control - image 17

Nonsmooth Mechanics Models Dynamics and Control - image 18

. In the following we shall prove that

whereas if is not zero then neither is We have 13 where - photo 20

is not zero, then neither is We have 13 where represents the derivative of - photo 21

. We have:

(1.3)

where

represents the derivative of

calculated ignoring the points of discontinuity of

, and which is not defined at the points of discontinuity [1082, Chap. 2, Sect. 3]. For instance, the distributional derivative of the heavyside function

for

for is The notation Dh instead of - photo 27

for is The notation Dh instead of is generally - photo 28

for

is The notation Dh instead of is generally used to denote the - photo 29

The notation Dh instead of is generally used to denote the distributional - photo 30

. The notation Dh instead of is generally used to denote the distributional derivative of a function h - photo 31

Light

Font size:

↓

↑

Reset

Interval:

↓

↑

Bookmark:

Make

Similar books «Nonsmooth Mechanics : Models, Dynamics and Control»

Look at similar books to Nonsmooth Mechanics : Models, Dynamics and Control. We have selected literature similar in name and meaning in the hope of providing readers with more options to find new, interesting, not yet read works.

Harendra Singh (editor)

Methods of Mathematical Modelling: Fractional Differential Equations (Mathematics and its Applications)

Masoud Karimi-Ghartemani

Modeling and Control of Modern Electrical Energy Systems

Ziyang Meng

Modelling, Analysis, and Control of Networked Dynamical Systems

Xiaodi Li

Impulsive Systems with Delays: Stability and Control

N. U. Ahmed

Optimal Control of Dynamic Systems Driven by Vector Measures: Theory and Applications

Hiroshi Yabuno

Linear and Nonlinear Instabilities in Mechanical Systems: Analysis, Control and Application

Zhikang Shuai

Transient Characteristics, Modelling and Stability Analysis of Microgird

Salinelli Ernesto

Discrete Dynamical Models

Devaney Robert L.

Differential Equations, Dynamical Systems, and an Introduction to Chaos

Adil Bagirov Napsu Karmitsa

Introduction to Nonsmooth Optimization

Francis Clarke

Functional Analysis, Calculus of Variations and Optimal Control

Andrew Kurdila

Dynamics and Control of Robotic Systems

Reviews about «Nonsmooth Mechanics : Models, Dynamics and Control»

Discussion, reviews of the book Nonsmooth Mechanics : Models, Dynamics and Control and just readers' own opinions. Leave your comments, write what you think about the work, its meaning or the main characters. Specify what exactly you liked and what you didn't like, and why you think so.