2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h)
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- ねんたろう さくいし
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1 a a a 1 1 1
2 2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h)
3 5 2.4 x y (x,y) l a x = l cot h cos a, (3) y = l cot h sin a (4) h a h a x y x y 5 3
4 (3) (4) x y (x + e2 tan φ ) 2 y 2 1 e 2 l + 1 e 2 = l 2 ( ) (1 e 2 ) 2 e 2 sec 2 φ 1 6 φ e φ δ 7 e cos φ (6) sin δ e (5) (5) (1 e 2 )x 2 + 2l e 2 tan φ x + y 2 + l 2 (1 e 2 tan 2 φ) = 0 (7) (5) (7) e 1) e = 0,, x 2 + y 2 = l 2 ( ) 2) 0 < e < 1,, x + e2 tan φ 2 ) l 1 e + y 2 = (e l2 2 1 e 2 (1 e 2 ) 2 sec 2 φ 1 2 3) e = 1,, 2l tan φ x + y 2 + l 2 (1 tan 2 φ) = 0 ( ) 4) 1 < e <,, x e2 tan φ 2 l y 2 e 2 1 5) e =,, x = l tan φ e 2 1 = (e l2 (e 2 1) 2 sec 2 φ 1 2 (6) φ e φ δ e ) (5) e = 0 (φ = 90, δ > 0 ) (φ = 90, δ < 0 ) e = 0 l e = (δ = 0 ( e = ) x = l tan φ 6 Appendix 7 4
5 φ δ e e φ δ ( φ > 66.5 ) δ 23.5 δ cm 5.0 cm h 12 (1) cot h 12 = L l = 2.0 = 0.4 (8) 5.0 h 12 = φ δ φ + δ = ( e = 1) e = 1 e = , 10 11, 11 12, 12 13, (13 14, (
6 1: x y (x i, y i ) i 9 i = 1 16 i = cm 6
7 (l = 5cm) i x i (cm) y i (cm) X i (= x i /l) Y i (= y i /l) (7) (7) X Y X x l, Y y l (9) (7) X, Y (1 e 2 )X 2 + 2e 2 tan φ X + Y 2 + (1 e 2 tan 2 φ) = 0 (10) l (10) 7
8 (10) φ φ δ e tan φ = e X i, Y i (i = 1, 2,, 27) e 2 e 2 = 27 i=1 {(X2 i 2X i tan φ + tan 2 φ)(xi 2 + Y i 2 + 1)} 27 i=1 (X2 i 2X i tan φ + tan 2 = (11) φ) 2 e e( ) = 3.30 (12) e = 3.30 (6) (12) δ( ) δ( ) = (13) (2004 δ( ) δ( ) = (14) Appendix δ > 0) 14 8
9 2: 4.1 l L = 3.8cm x y
10 4.3 x y (x i, y i ), i = 1, 2,, 27, l (X i, Y i ) 4.4 (11) (X i, Y i ), i = 1, 2,, 27, e 8 12 δ (δ = ) (5) : a : h : δ φ 10
11 l (x, y) x = l cot z cos a y = l cot z sin a (15) x y z a (δ, H) H δ (h, a) (δ, H) cos h sin a = cos δ sin H, cos h cos a = sin δ cos φ + cos δ sin φ cos H, (16) sin h = sin δ sin φ + cos δ cos φ cos H cos δ sin H cot h sin a = sin δ sin φ + cos δ cos φ cos H, cot h cos a = sin δ cos φ + cos δ sin φ cos H sin δ sin φ + cos δ cos φ cos H (17) X x sin δ cos φ + cos δ sin φ cos H = l sin δ sin φ + cos δ cos φ cos H, (18) Y y l = cos δ sin H sin δ sin φ + cos δ cos φ cos H (19) X Y H (sin φ X cos φ) cos δ sin H = Y sin δ (sin φ X cos φ) cos δ cos H = X sin δ sin φ + sin δ cos φ (20) sin H cos H X 2 (sin 2 δ cos 2 φ) + 2X sin φ cos φ + Y 2 sin 2 δ + sin 2 δ cos 2 φ cos 2 δ sin 2 φ = 0 (21) sin 2 δ cos 2 φ sin 2 δ = cos 2 φ 11
12 5.1 sin 2 δ cos 2 φ ( X + sin φ cos φ ) 2 sin 2 δ + (sin 2 δ cos 2 φ) (sin 2 δ cos 2 φ) Y 2 = sin 2 δ cos 2 δ (sin 2 δ cos 2 φ) 2 (22) sin δ = 0 X = tan φ = const. (23) (19) Y = tan H cos φ (24) Y X (18) (X = tan φ) sin δ = 0 δ = 0 λ sin δ = sin λ sin ɛ (25) ɛ sin δ = 0 sin λ = 0 λ = 0, π sin δ 0 (X + e2 tan φ) 2 Y e 2 (1 e 2 ) = cot2 δ (1 e 2 ) 2 = 1 ( ) (1 e 2 ) 2 e 2 sec 2 φ 1 (26) e e cos φ sin δ e 2 (27) 5.2 sin 2 δ = cos 2 φ Y 2 + 2X tan φ + (1 tan 2 φ) = 0 (28) 12
13 6 (10) (X i, Y i ) (1 e 2 )X 2 i + 2e 2 X i tan φ + Y 2 i + (1 e 2 tan 2 φ) = 0 (29) (X i, Y i ) (29) ξ i (1 e 2 )X 2 i + 2e 2 X i tan φ + Y 2 i + (1 e 2 tan 2 φ) = X 2 i + Y 2 i + 1 e 2 (X 2 i 2X i tan φ + tan 2 φ), i = 1, 2,, 27 (30) ξ i (30) φ ξ i e 2 S(e 2 ) S(e 2 27 ) ξi 2 (31) i=1 e 2 e 2 (30) ξ i S(e 2 ) = [ 27 i=1 [ 27 2 (X 2 i 2X i tan φ + tan 2 φ) 2] (e 2 ) 2 ] (Xi 2 2X i tan φ + tan 2 φ)(xi 2 + Y 2 + 1) e (Xi 2 + Yi 2 + 1) (32) 2 i=1 i=1 e 2 (e 2 ) 2 e 2 e 2 = 27 i=1 (X2 i 2X i tan φ + tan 2 φ)(xi 2 + Y 2 + 1) 27 i=1 (X2 i 2X i tan φ + tan 2 (33) φ) 2 S(e 2 ) e 2 (33) 13
() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)
0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()
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145 13 13.1 13.1.1 0 m mg S 13.1 F 13.1 F /m S F F 13.1 F mg S F F mg 13.1: m d2 r 2 = F + F = 0 (13.1) 146 13 F = F (13.2) S S S S S P r S P r r = r 0 + r (13.3) r 0 S S m d2 r 2 = F (13.4) (13.3) d 2
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38 5 Cauchy.,,,,., σ.,, 3,,. 5.1 Cauchy (a) (b) (a) (b) 5.1: 5.1. Cauchy 39 F Q Newton F F F Q F Q 5.2: n n ds df n ( 5.1). df n n df(n) df n, t n. t n = df n (5.1) ds 40 5 Cauchy t l n mds df n 5.3: t
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13 13.1 O r F R = m d 2 r dt 2 m r m = F = m r M M d2 R dt 2 = m d 2 r dt 2 = F = F (13.1) F O L = r p = m r ṙ dl dt = m ṙ ṙ + m r r = r (m r ) = r F N. (13.2) N N = R F 13.2 O ˆn ω L O r u u = ω r 1 1:
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