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Classical Dynamics of Particles and Sys...

5th Edition

Stephen T. Thornton, Jerry B. Marion

Publisher: Cengage Learning

ISBN: 9780534408961

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Chapter

Section

Problem 1.1P:

Find the transformation matrix that rotates the axis x3 of a rectangular coordinate system 45°...

Problem 1.3P:

Find the transformation matrix that rotates a rectangular coordinate system through an angle of 120...

Problem 1.4P:

Show
(a) (AB)t = BtAt (b) (AB)−1 = B−1 A−1

Problem 1.5P:

Show by direct expansion that |λ|2 = 1. For simplicity, take λ to be a two-dimensional orthogonal...

Problem 1.6P:

Show that Equation 1.15 can be obtained by using the requirement that the trans-formation leaves...

Problem 1.7P:

Consider a unit cube with one corner at the origin and three adjacent sides lying along the three...

Problem 1.8P:

Let A be a vector from the origin to a point P fixed in space. Let r be a vector from the origin to...

Problem 1.9P:

For the two vectors
find
A − B and |A – B|
component of B along A
angle between A and B
A × B
(A −...

Problem 1.10P:

A particle moves in a plane elliptical orbit described by the position vector r=2bsinti+bcostj (a)...

Problem 1.11P:

Show that the triple scalar product (A B) C can be written as (AB)C=|A1A2A3B1B2B3C1C2C3| Show also...

Problem 1.12P:

Let a, b, c be three constant vectors drawn from the origin to the points A, B C. What is the...

Problem 1.13P:

X is an unknown vector satisfying the following relations involving the known vectors A and B and...

Problem 1.14P:

Consider the following matrices: A=(121031201),B=(210012113),C=(214310) Find the following (a) |AB|...

Problem 1.16P:

What surface is represented by r a = const, that is described if a is a vector of constant...

Problem 1.17P:

Obtain the cosine law of plane trigonometry by interpreting the product (A B) (A B) and the...

Problem 1.18P:

Obtain the sine law of plane trigonometry by interpreting the product A × B and the alternate...

Problem 1.19P:

Derive the following expressions by using vector algebra: (a) cos ( ) = cos cos + sin sin (b)...

Problem 1.20P:

1-20. Show that

Problem 1.21P:

Show (see also Problem 1–11) that

Problem 1.22P:

1-22. Evaluate the sum (which contains 3 terms) by considering the result for all possible...

Problem 1.24P:

Let A be an arbitrary vector, and let e be a unit vector in some fixed direction. Show that
What is...

Problem 1.26P:

1-26. A particle moves with v = const. along the curve r — k(1 + cos θ) (a cardioid). Find

Problem 1.27P:

If r and are both explicit functions of time, show that

Problem 1.28P:

Show that

Problem 1.29P:

Find the angle between the surfaces defined by r2 = 9 and x + y + z2 = 1 at the point (2, −2, 1).

Problem 1.30P:

Show that ∇(ϕψ) = ϕ∇ψ + ψ∇ϕ.

Problem 1.31P:

Show that
(a)
(b)
(c)

Problem 1.32P:

Show that (2arr+2brr)dt=ar2+br2+const. where r is the vector from the origin to the point (x1, x2,...

Problem 1.33P:

Show that (rrrrr2)dt=rr+C where C is a constant vector.

Problem 1.34P:

Evaluate the integral

Problem 1.35P:

Show that the volume common to the intersecting cylinders defined by x2 + y2 = a2 and x2 + z2 = a2...

Problem 1.36P:

Find the value of the integral sA da, where A = xi yj + zk and S is the closed surface defined by...

Problem 1.37P:

Find the value of the integral s A da, where A = (x2 + y2 + z2)(xi + yj + zk) and the surface S is...

Problem 1.38P:

Find the value of the integral S( A) da if the vector A = yi + zj + xk and S is the surface...

This best-selling classical mechanics text, written for the advanced undergraduate one- or two-semester course, provides a complete account of the classical mechanics of particles, systems of particles, and rigid bodies. Vector calculus is used extensively to explore topics. The Lagrangian formulation of mechanics is introduced early to show its powerful problem solving ability.. Modern notation and terminology are used throughout in support of the text's objective: to facilitate students' transition to advanced physics and the mathematical formalism needed for the quantum theory of physics. CLASSICAL DYNAMICS OF PARTICLES AND SYSTEMS can easily be used for a one-or two-semester course, depending on the instructor's choice of topics.

New to the Edition

- New problems and examples have been added to provide students with ample opportunity to master the material.

- The Fifth Edition features a classic and accessible design to engage today's visually oriented students.

- To reinforce and enhance the connection between important content points and supporting visuals, new FIGURE CAPTIONS accompany the text art.

Features

- Written for maximum flexibility, this best-selling junior level mechanics text is easily adaptable to any length-one-or two-semester-or focus of course.

- LAGRANGIAN and HAMILTONIAN DYNAMICS are introduced early in the text.

- This text has an entire chapter on NONLINEAR METHODS.

- NUMERICAL METHODS PROBLEMS are included for students to solve using a computer.

We offer sample solutions for Classical Dynamics of Particles and Systems homework problems. See examples below:

Find the transformation matrix that rotates the axis x3 of a rectangular coordinate system 45°...Suppose that the force acting on a particle is factorable into one of the following forms:
F(xi, t)...A simple harmonic oscillator consists of a 100-g mass attached to a spring whose force constant is...

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