Vector analysis including the dynamics of a rigid body:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Oxford Univ. Press
1962
|
| Schriftenreihe: | Oxford mathematical handbooks
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 192 S. graph. Darst. 22 cm |
Internformat
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| 264 | 1 | |a London [u.a.] |b Oxford Univ. Press |c 1962 | |
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Datensatz im Suchindex
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| adam_text | Contents
PREFACE v
1. INTRODUCTION. ADDITION AND SUBTRACTION 1
Real number system, Geometry, analysis, scalars, vectors, and the real
number system. Advantages of vector analysis in the field theories of
science. Addition and subtraction of vectors. Vector equation of a
straight line. Worked examples. Cartesian components of a vector.
Direction cosines and ratios. Distance between two points. Cartesian
equation of a line. Worked examples. Linear dependence. Equation of
a plane through three points. Exercises.
2. SCALAR PRODUCT. CROSS PRODUCT. TRIPLE PRO¬
DUCTS 35
Work done by a force. Scalar product. Distributive law. Worked
examples including the general equation of a plane. Line integrals.
Conservative forces. Potential energy. Positions of equilibrium. Moment
vector. Cross product. Angular velocity vector. Area vector. Distribu¬
tive law. Worked examples. Triple scalar and vector products. Exercises.
3. DIFFERENTIATION OF VECTORS 62
Derivative of a vector. Instantaneous velocity and acceleration. Differ¬
entiation formulae. Worked examples including the stability of a
conservative system of force. Derivative of a unit vector. Velocity and
acceleration in polar co ordinates. Tangential and normal components
of acceleration. Curvature. Total and local rates of change. Exercises.
4. VECTOR CALCULUS. DIVERGENCE. GRADIENT.
CURL 76
Point functions. Surface and volume integrals. Fluid flow and div q.
Divergence of a vector. Div F in co ordinate form. Gauss s divergence
theorem and reason for its usefulness. Continuity equation. Fluid flow
and grad p. Gradient of a scalar function. Grad j in co ordinate form.
Operator v Total rate of change. Level surfaces. Grad f and maximum
rate of change of f . Worked examples including tangent plane to a
surface. Heat conduction equation. Conservative vector functions. CurlF.
Curl F in co ordinate form. Worked examples. Summary and compre¬
hensive definition. Curl Fin terms of a maximum line integral. Stokes s
theorem for simply and multiply connected regions. Worked examples.
Curl grad 4 . Div curl F. Div grad t . Curl curl F. Worked examples.
Exercises.
5. OPERATOR TECHNIQUES. ORTHOGONAL CURVI¬
LINEAR CO ORDINATES 128
V operating on products. Worked examples. Green s theorem and rea¬
sons for its usefulness. Orthogonal curvilinear co ordinates. Cylindrical
and spherical polar co ordinates. Div, grad, curl and V2 in orthogonal
curvilinear co ordinates. Differentiation of unit vectors. Exercises.
vii
viii CONTENTS
6. FUNCTIONAL ASPECTS OF SCIENTIFIC CONCEPTS
AND THEORIES. NEWTONIAN MECHANICS. MOTION
OF A SYSTEM OF PARTICLES AND OF A RIGID BODY 149
Discussion of the functional nature of the concepts of science. Greek
failure to deal with motion. Galileo s solution through the formulation
of new concepts. Newton s laws of motion. Solution of problems in
Newtonian mechanics.
Linear and angular motion of a system of particles. Kinetic energy.
Moments of inertia. Motion of a rigid body about a fixed axis. Two
dimensional motion of a rigid body. Rolling and slipping. Worked
examples. Conservation of linear momentum, moment of momentum
and energy. Worked examples. Impulsive motion. Worked examples.
Impact of elastic bodies. Exercises.
ANSWERS TO THE EXERCISES 190
INDEX 191
|
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| id | DE-604.BV009048987 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:29:14Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005989093 |
| oclc_num | 1191898578 |
| open_access_boolean | |
| owner | DE-29T DE-11 DE-83 DE-210 |
| owner_facet | DE-29T DE-11 DE-83 DE-210 |
| physical | VIII, 192 S. graph. Darst. 22 cm |
| psigel | HUB-ZB011201110 |
| publishDate | 1962 |
| publishDateSearch | 1962 |
| publishDateSort | 1962 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series2 | Oxford mathematical handbooks |
| spelling | Smith, Gordon D. Verfasser (DE-588)1158286333 aut Vector analysis including the dynamics of a rigid body G. D. Smith London [u.a.] Oxford Univ. Press 1962 VIII, 192 S. graph. Darst. 22 cm txt rdacontent n rdamedia nc rdacarrier Oxford mathematical handbooks Dynamics Vector analysis Dynamik (DE-588)4013384-9 gnd rswk-swf Stereostatik (DE-588)1137527986 gnd rswk-swf Bewegung (DE-588)4006311-2 gnd rswk-swf Vektoranalysis (DE-588)4191992-0 gnd rswk-swf Vektoranalysis (DE-588)4191992-0 s DE-604 Stereostatik (DE-588)1137527986 s Dynamik (DE-588)4013384-9 s Bewegung (DE-588)4006311-2 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005989093&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Smith, Gordon D. Vector analysis including the dynamics of a rigid body Dynamics Vector analysis Dynamik (DE-588)4013384-9 gnd Stereostatik (DE-588)1137527986 gnd Bewegung (DE-588)4006311-2 gnd Vektoranalysis (DE-588)4191992-0 gnd |
| subject_GND | (DE-588)4013384-9 (DE-588)1137527986 (DE-588)4006311-2 (DE-588)4191992-0 |
| title | Vector analysis including the dynamics of a rigid body |
| title_auth | Vector analysis including the dynamics of a rigid body |
| title_exact_search | Vector analysis including the dynamics of a rigid body |
| title_full | Vector analysis including the dynamics of a rigid body G. D. Smith |
| title_fullStr | Vector analysis including the dynamics of a rigid body G. D. Smith |
| title_full_unstemmed | Vector analysis including the dynamics of a rigid body G. D. Smith |
| title_short | Vector analysis including the dynamics of a rigid body |
| title_sort | vector analysis including the dynamics of a rigid body |
| topic | Dynamics Vector analysis Dynamik (DE-588)4013384-9 gnd Stereostatik (DE-588)1137527986 gnd Bewegung (DE-588)4006311-2 gnd Vektoranalysis (DE-588)4191992-0 gnd |
| topic_facet | Dynamics Vector analysis Dynamik Stereostatik Bewegung Vektoranalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005989093&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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