Read e-book online Analytical Elements of Mechanics. Dynamics PDF

By Thomas R. Kane

ISBN-10: 1483227898

ISBN-13: 9781483227894

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By Thomas R. Kane

ISBN-10: 1483227898

ISBN-13: 9781483227894

Show description

Read Online or Download Analytical Elements of Mechanics. Dynamics PDF

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Extra info for Analytical Elements of Mechanics. Dynamics

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I) at (k X n) X (k X nQ άθ = (k X n) - i ^ k M (k X n) · n' dt (k X n) · n' dt or Thus c = k atf œ \t* = —5k r a d s e c - 1 c D SECS. 1) can always be expressed in the form R 'o)R = R 'œR n0 where n0 is a unit vector parallel to κ'ωκ and κ'ωκ is a scalar, called the angular speed of R in R' for the direction n0, which is positive when R,o)R and n0 have the same sense, vanishes when R'coR is equal to zero, and is negative when the sense of κ'ωκ is opposite to that of n 0 . 3, determine the angular speed of D in C at time t* for (a) the k direction and (b) the — k direction, k being the unit vector shown in Fig.

Proof: Let n be a unit vector parallel to L. 1) . X (k x n) n) . 3) d< k X t k X n J d * "d* Hence Ä 'dn v , Ä'd ' | * χ . , . - * χ . , χ . ( | ) · di Χ 1 ( | ) · while Thus 'f-»x-)-*x-)-*x-)S-S di R R It follows from Sec. 2 that '

1) and can therefore be expressed in the form P = pv (1) where p is an intrinsically positive quantity, p is called the radius of curvature of C at P , and is given by SEC. 3 Diff. of Vectors] ρ ΙΡ' 41 (2) x P"| Proof: Multiply the numerator and denominator of the expression for p given in Sec. 1. 3) 1 R A dp ~ds J (A) SEC. 2) and λ, called the torsion of the curve C at point P, is given by R 9T dp L ds R 2 dp ds2 R d*pl ds*J SEC. 1 Difi. of Vectors] 43 The expressions (1), (2), and (3) are called the Serret-Frenet formulas.

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Analytical Elements of Mechanics. Dynamics by Thomas R. Kane

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