Read e-book online Analytical Elements of Mechanics PDF

By Thomas R. Kane

ISBN-10: 1483231283

ISBN-13: 9781483231280

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Problem: Find Fi, the m resolute of the force F shown in Fig. 11c. 56η! 15 The vector (cross) product of a vector a and a vector b: a X b Definition: a x b Ξ= jo| |b| sin (a, b)n where n is a unit vector whose direction is the same as the direction of advance of a right-handed screw rotated from a toward b, through the angle (a, b), when the axis of the screw is perpendic­ ular to both a and b. Examples: See Fig. 15. ^ ^ K / \ / '/ / \ / \ r ρη /^ '/ \/° '"axb ~~^7 ^ / ~ ^axb \ y *oxb axb FIG. 7).

I = 1, . . 6) n Σ (n*v*n) t= l while the L resolute of the resultant of the vectors vt, i = 1, 2 , . . 3. 8 Given n vectors vt, i = 1, . . , n, the resultant of the resolutes of these vectors perpendicular to a line L is equal to the resolute of the vectors' resultant perpendicular to L. 9 Every vector v can be expressed in the form v = niVFii + n 2 vn 2 + n 3 vn 3 where ni, n2, n3 are mutually perpendicular unit vectors. 2) Dot multiply both sides of Eq. 3) But, ηι·ηι = 1 and Πι*Ι12 = 111 * Ü3 = 0 Hence, ηι·ν = vi Similarly, n 2 v = v2 and n 3 v = vz Substitute into Eq.

9 Every vector v can be expressed in the form v = niVFii + n 2 vn 2 + n 3 vn 3 where ni, n2, n3 are mutually perpendicular unit vectors. 2) Dot multiply both sides of Eq. 3) But, ηι·ηι = 1 and Πι*Ι12 = 111 * Ü3 = 0 Hence, ηι·ν = vi Similarly, n 2 v = v2 and n 3 v = vz Substitute into Eq. (1). 12). However, when v is resolved into three components parallel to mutually perpendicular unit vectors nt, i = 1, 2, 3, the n t component of v is equal to the n» resolute of v. 6, nrvih is equal to the ni resolute of v.

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Analytical Elements of Mechanics by Thomas R. Kane


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