Mathematic Methods HW Solutions 48

Mathematic Methods HW Solutions 48 - Chapter 9 6.1 6.4...

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Unformatted text preview: Chapter 9 6.1 6.4 catenary catenary 8.2 I= 8.3 I= 8.4 I= 48 6.2 6.5 x2 y 2 1+y y dy 2 x2+1 circle circle 6.3 6.6 circular cylinder circle dx, x2 (2y + y 3 ) = K (1 + y 2 )3/2 2 2 , x y 2 = C 2 (1 + x )3 r2 + r4 θ 2 dr , dr dθ √ = Kr r4 − K 2 y = aebx (x − a)2 + (y + 1)2 = C 2 (y − b)2 = 4a2 (x + 1 − a2 ) Intersection of r = 1 + cos θ with z = a + b sin(θ/2) Intersection of the cone with r cos(θ sin α + C ) = K √ Intersection of y = x2 with az = b[2x 4x2 + 1 + sinh−1 2x] + c 8.12 ey cos(x − a) = K r = K sec2 θ+c 2 32 2 2 (x + 2 ) + (y − b) = c 8.14 (x − a)2 = 4K 2 (y + 2 − K 2 ) √ 3 8.15 y + c = 2 K x1/3 x2/3 − K 2 + K 2 cosh−1 (x1/3 /K ) 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.13 8.16 8.17 8.18 8.19 8.20 8.21 8.22 8.23 8.25 8.26 8.27 8.28 Hyperbola: r2 cos(2θ + α) = K or (x2 − y 2 ) cos α − 2xy sin α = K K ln r = cosh(Kθ + C ) Parabola: (x − y − C )2 = 4K 2 (x + y − K 2 ) ˙ ˙ m(¨ − rθ2 ) + kr = 0, r2 θ = const. r ˙2 ) + K/r2 = 0, r2 θ = const. ˙ m(¨ − rθ r 2 2˙ ˙ r − rθ = 0, r θ = const., z + g = 0 ¨ ¨ 1 2¨ ˙ − r2 sin θ cos θ φ2 ) = − 1 ∂V = Fθ = maθ ˙ ˙ r · m(r θ + 2rr θ r ∂θ ¨ + 2rθ − r sin θ cos θ φ2 ˙ ˙ aθ = r θ ˙ 1 ˙ ¨ L = 2 ma2 θ2 − mga(1 − cos θ), aθ + g sin θ = 0, θ measured from the downward direction. √ l = 2 πA r = Aebθ dr = r K 2 (1 + λr)2 − 1 dθ dA 1˙ ˙ ˙ r2 θ = const., |r × mv| = mr 2 θ = const., = r2 θ = const. dt 2 ...
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This note was uploaded on 02/29/2012 for the course MHF 2312 taught by Professor Dr.chet during the Fall '11 term at UNF.

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