Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 1, Problem 1.23P
Use the εijk notation and derive the identity
(A × B) × (C × D) = (ABD)C − (ABC)D
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Suppose thatP = (x, y) has polar coordinates(r, θ ). Find the polarcoordinates for the points:
(−x, y)
prove that A ⊕ B
Equal to inverse of Y= ĀB+AB̄
Given P(47, 169 deg, 153 deg) in spherical coordinate system, what is y in rectangular coordinates of P?
Given P(5, -49, -15) in rectangular coordinate system, what is Φ (phi) in spherical coordinates of P in degrees?
Given P(31, 63 deg, -132 deg) in spherical coordinate system, what is z in rectangular coordinates of P?
(Compute up to 4 decimal places)
Chapter 1 Solutions
Classical Dynamics of Particles and Systems
Ch. 1 - Prob. 1.1PCh. 1 - 1.2. Prove Equations 1.10 and 1.11 from...Ch. 1 - Prob. 1.3PCh. 1 - Show
(a) (AB)t = BtAt (b) (AB)−1 = B−1 A−1
Ch. 1 - Prob. 1.5PCh. 1 - Prob. 1.6PCh. 1 - Consider a unit cube with one corner at the origin...Ch. 1 - Prob. 1.8PCh. 1 - For the two vectors
find
A − B and |A –...Ch. 1 - A particle moves in a plane elliptical orbit...
Ch. 1 - Prob. 1.11PCh. 1 - Let a, b, c be three constant vectors drawn from...Ch. 1 - X is an unknown vector satisfying the following...Ch. 1 - Prob. 1.14PCh. 1 - Prob. 1.15PCh. 1 - What surface is represented by r a = const, that...Ch. 1 - Obtain the cosine law of plane trigonometry by...Ch. 1 - Obtain the sine law of plane trigonometry by...Ch. 1 - Prob. 1.19PCh. 1 - 1-20. Show that
Ch. 1 - Show (see also Problem 1–11) that
Ch. 1 - Prob. 1.22PCh. 1 - Use the εijk notation and derive the identity
(A ×...Ch. 1 - Prob. 1.24PCh. 1 - Find the components of the acceleration vector a...Ch. 1 - Prob. 1.26PCh. 1 - If r and are both explicit functions of time,...Ch. 1 - Show that
Ch. 1 - Prob. 1.29PCh. 1 - Prob. 1.30PCh. 1 - Show that
(a)
(b)
(c)
Ch. 1 - Show that (2arr+2brr)dt=ar2+br2+const. where r is...Ch. 1 - Show that (rrrrr2)dt=rr+C where C is a constant...Ch. 1 - Prob. 1.34PCh. 1 - Prob. 1.35PCh. 1 - Prob. 1.36PCh. 1 - Prob. 1.37PCh. 1 - Prob. 1.38PCh. 1 - A plane passes through the three points (x, y, z)...Ch. 1 - For what values of a are the vectors A = 2ai − 2j...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Is it possible for to be smaller than unity? `arrow_forwardObtain the sine law of plane trigonometry by interpreting the product A × B and the alternate representation (A − B) × B.arrow_forwardRectangular coordinates of a point are given by (2,y) and its polar coordinates are given by (r,/6) . Find y y and r .arrow_forward
- Two points in the xy plane have Cartesian coordinates (2.00, 4.00) m and (3.00, 3.00) m. Determine (a) the distance between these points and (b) their polar coordinates.arrow_forwardin the general linear equation y=bx+a, what is measured by the value of b?arrow_forwardFind the angle between A = 3i+j and B= 3i+3jarrow_forward
- I kept doing the calculation in the calculator and wasn't getting the correct answer, can you help? two points are given in polar coordinates by (r, ?) = (2.20 m, 50.0°) and (r, ?) = (3.00 m, −60.0°) , respectively. What is the distance between them?arrow_forwardConvert the equation z=x²+y² to spherical coordinatesarrow_forwardGIVEN: A= 5.00i + 2.00j B =3.00i + 1.00j – 3.00k C = 2.00i + 8.00j Find B x (AxC)arrow_forward
- I keep trying to combine these equations but whenever I do so I get a negative in the square root. Please help.arrow_forwardFor an angle, u measured from the positive x - axis, the valuesof sin u and cos u are always (choose one): (a) greater than +1(b) less than -1 (c) greater than -1 and less than 1 (d) greater than or equal to -1 and less than or equal to 1 (e) less than or equal to -1 or greater than or equal to 1.arrow_forwardHow many significant figures are there in (a) 0.0000303 and(b) 6.201 * 105?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Introduction to Vectors and Their Operations; Author: Professor Dave Explains;https://www.youtube.com/watch?v=KBSCMTYaH1s;License: Standard YouTube License, CC-BY