Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Elementary Particle Dynamics Read chapter Read first chapter

2019 | OriginalPaper | Chapter

6. Momenta, Impulses, and Collisions

Author : Oliver M. O’Reilly

Published in: Engineering Dynamics

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

As a prelude to the discussion of a system of particles, the linear and angular momenta of a single particle are introduced in this chapter. In particular, conditions for the conservation of these kinematical quantities are established. This is followed by a discussion of impact problems where particles are used as models for the impacting bodies.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Power, Work, and Energy
next chapter Dynamics of Systems of Particles
Footnotes
1
Johannes Kepler (1571–1630) was a German astronomer and physicist who, based on observations of the orbits of certain planets, proposed three laws to explain planetary motion. His three laws are the most famous of his many scientific contributions.
 
2
For further treatments of these equations, see, for example, Arnol’d [2] and Moulton [65]. Discussions of this central force problem can also be found in every undergraduate dynamics text, for example, in Meriam and Kraige [63, Section 13, Chapter 3] and Riley and Sturges [79, Section 15, Chapter 5]. You should notice that these texts assume that the motion of the particle is planar.
 
3
We leave it as an exercise to show that the total energy and angular momentum \(\mathbf{H}_O\cdot \mathbf{E}_z\) are also conserved when the spring is replaced by an inextensible string.
 
4
An example illustrating these three vectors is shown in Fig. 6.8. We also note that for many problems these vectors will coincide with the Cartesian basis vectors.
 
5
It should be clear that, given the preimpact velocity vectors, the balance laws only provide six equations from which one needs to determine the six postimpact velocities and the linear impulses of \(\mathbf{F}_{1_d}\) and \(\mathbf{F}_{1_r}\). The introduction of the coefficient of restitution e and the assumption of a common normal velocity \(v_{II}\) at time \(t = t_1\) gives two more equations that render the system of equations solvable. That is, these two additional equations close the system of equations.
 
6
The definition of the kinetic energy of a system of particles is discussed in further detail in Section 7.​2.​4 of Chapter 7.
 
7
The model we discuss is a prototypical example in control theory for illustrating Zeno behavior (see, e.g., Liberzon [60]). The term Zeno behavior is in reference to the Greek philosopher Zeno of Elea and his famous dichotomy paradox. He is perhaps more famous for his paradox about the tortoise and the hare.
 
Metadata
Title
Momenta, Impulses, and Collisions
Author
Oliver M. O’Reilly
Copyright Year
2019
Book
Engineering Dynamics

Print ISBN: 978-3-030-11744-3

Electronic ISBN: 978-3-030-11745-0

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-11745-0_6

Premium Partner

    Image Credits