Mathematical methods of classical mechanics by Tabachnikov S.

By Tabachnikov S.

Show description

Read or Download Mathematical methods of classical mechanics PDF

Best mathematical physics books

An Introduction to Chaos in Nonequilibrium Statistical Mechanics

This booklet is an creation to the purposes in nonequilibrium statistical mechanics of chaotic dynamics, and in addition to using options in statistical mechanics vital for an knowing of the chaotic behaviour of fluid structures. the basic options of dynamical platforms conception are reviewed and straightforward examples are given.

Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics

"José Ferreirós has written a magisterial account of the heritage of set thought that is panoramic, balanced, and fascinating. not just does this ebook synthesize a lot earlier paintings and supply clean insights and issues of view, however it additionally contains a significant innovation, a full-fledged remedy of the emergence of the set-theoretic procedure in arithmetic from the early 19th century.

Computational Physics: Problem Solving with Python

Using computation and simulation has turn into an important a part of the clinical procedure. with the ability to remodel a concept into an set of rules calls for major theoretical perception, unique actual and mathematical figuring out, and a operating point of competency in programming. This upper-division textual content offers an surprisingly wide survey of the themes of contemporary computational physics from a multidisciplinary, computational technological know-how perspective.

Additional resources for Mathematical methods of classical mechanics

Example text

When it operates on a scalar function, it turns ∇ϕ into a vector with definite magnitude and direction. It also has a definite physical meaning. 1. Show that ∇r = r and ∇f (r) = rdf /dr, where r is a unit vector along the position vector r = xi + yj + zk and r is the magnitude of r. 1. ∂ ∂ ∂ +j +k r, ∂x ∂y ∂z ∂ ix ix ∂r 1/2 =i x2 + y 2 + z 2 = = , i 1/2 2 2 2 ∂x ∂x r (x + y + z ) xi + yj + zk r ix jy kz + + = = = r. ∇r = r r r r r ∇r = i etc. ∂f ∂f ∂f +j +k , ∂x ∂y ∂z ∂f df ∂r df x i =i =i , etc.

10i + 3j + 11k, −10i − 3j − 11k. 8. Find the area of a parallelogram having diagonals A = 3i + j − 2k and B=i− √ 3j + 4k. Ans. 5 3. 9. Evaluate (2i − 3j) · [(i + j − k) × (3j − k)]. Ans. 4. 10. Find the volume of the parallelepied whose edges are represented by A = 2i − 3j + 4k, B = i + 2j − k, and C = 3i − j + 2k. Ans. 7. 11. Find the constant a such that the vectors 2i − j + k, i + 2j − 3k and 3i + aj + 5k are coplanar. Ans. a = −4. 12. Show that (a) (b × c) × (c × a) = c (a · b × c) ; 2 (b) (a × b) · (b × c) × (c × a) = (a · b × c) .

To find the perpendicular distance between them is a difficult problem in analytical geometry. With vectors, it is relatively easy. Let the equations of two such lines be r = r1 + tv1 , r = r2 + t v2 . 3 Lines and Planes 25 Let a on line 1 and b on line 2 be the end points of the common perpendicular on these two lines. 47) with t = t2 . Accordingly ra = r1 + t1 v1 , rb = r2 + t2 v2 . 49) Since rb − ra is perpendicular to both v1 and v2 , it must be in the direction of (v1 × v2 ) . If d is the length of rb − ra , then rb − ra = v1 × v2 d.

Download PDF sample

Rated 4.72 of 5 – based on 11 votes