- 1、本文档共27页,可阅读全部内容。
- 2、有哪些信誉好的足球投注网站(book118)网站文档一经付费(服务费),不意味着购买了该文档的版权,仅供个人/单位学习、研究之用,不得用于商业用途,未经授权,严禁复制、发行、汇编、翻译或者网络传播等,侵权必究。
- 3、本站所有内容均由合作方或网友上传,本站不对文档的完整性、权威性及其观点立场正确性做任何保证或承诺!文档内容仅供研究参考,付费前请自行鉴别。如您付费,意味着您自己接受本站规则且自行承担风险,本站不退款、不进行额外附加服务;查看《如何避免下载的几个坑》。如果您已付费下载过本站文档,您可以点击 这里二次下载。
- 4、如文档侵犯商业秘密、侵犯著作权、侵犯人身权等,请点击“版权申诉”(推荐),也可以打举报电话:400-050-0827(电话支持时间:9:00-18:30)。
查看更多
J. Nonlinear Sci. Vol. 16: pp. 255–281 (2006)
DOI: 10.1007/s00332-005-0691-8
© 2006 Springer Science+Business Media, Inc.
Static Equilibria of Rigid Bodies: Dice, Pebbles,
and the Poincar´e-Hopf Theorem
P. L. V´arkonyi and G. Domokos
Budapest University of Technology and Economics, Department of Mechanics, Materials and
Structures, H-1111 Muegyetem rkp. 1-3, Budapest, Hungary
and
Center for Applied Mathematics and Computational Physics, Budapest, Hungary
vpeter@mit.bme.hu
domokos@bagira.iit.bme.hu
Received February 1 , 2005; revised manuscript accepted for publication January 23, 2006
Online publication May 22, 2006
Communicated by J. E. Marsden
Summary. By appealing to the Poincar´e-Hopf Theorem on topological invariants, we
introduce a global classification scheme for homogeneous, convex bodies based on the
number and type of their equilibria. We show that beyond trivially empty classes all other
classes are non-empty in the case of three-dimensional bodies; in particular we prove
the existence of a body with just one stable and one unstable equilibrium. In the case
of two-dimensional bodies the situation is radically different: the class with one stable
and one unstable equilibrium is empty (Domokos, Papadopoulos, Ruina, J. Elasticity 36
[1994], 59–66). We also show that the latter result is equivalent to the classical Four-
Vertex Theorem in differential geometry. We illustrate the introduced equivalence classes
by various types of dice and statistical experimental results concerning pebbles on the
seacoast.
Key words. Static equilibria, rigid bodies, monostatic bodies, pebble shapes.
MSC numbers. 74G55, 37J05.
1. Introduction
In this paper we study the number and type of static equilibria of homogeneous, convex
bodies resting on a horizontal surface without friction in the presence of uniform gravity.
Static equilibria of rigid bodies have been
您可能关注的文档
- Computer VisionComputing And Visualization In Science英文电子书.pdf
- Hyperthermia in cancer therapy where are we today and where are we going英文电子书.pdf
- Synthesizable IP Core for WIMAX 802 16E LDPC Code Decoding英文电子书.pdf
- Sound On Sound Recording the Acoustic Guitar英文电子书.pdf
- Kass Miller Rapid stable fluid dynamics for computer graphics英文电子书.pdf
- Tackling External Fraud英文电子书.pdf
- Type Theoretic Foundations For Concurrent Object Oriented Programing英文电子书.pdf
- Paparazzi Platform Flexible Open Source UAS Software and Hardware英文电子书.pdf
- Shoulders and Sarfatti Energy Conversion From The Exotic Vacuum英文电子书.pdf
- Creative Science and Research Fuelless Gravity Engine英文电子书.pdf
文档评论(0)