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N 1) 2) 3) 4) 5) 6) 1) 2) 1) 2) 3) 4) 5) 6) 7) 8) xn = f (xn-1) 1) 2) z = |f(r)-r| z = |Mapn(x) - x| (1) 3) 4) 5) 6) H (p1, p2, q1, q2 = const) = = E = const 7) 8) 9) 1) 2) 3) 4) 5) y(x) = f(y, x), y Rn, x R.

yn+1 := y(xn+1) yn := y(xn) 1) f(x, y) s > 4 s 2) 3) I = E mv = N + F, (I). = a N + MF, (2) v + a = 0. (3) m v I = E a R N F MF G Q N M = -R-1a = D ( ) + MF, + R = R, (4) D = mR2 r F (r) M = + D ( ), =, (5) |F (r)| F (r) = 0 U(r + + R) 1(M H =, ) + U(r + R), F1 = 2 = 1. (6) 2 F (r) = 0 (4) r1 = (f(3) - R)1, r2 = (f(3) - R)2, 2 (7) 1 - 3 r3 = f(3) - f(3) d3 - R3, 3 f(3) (7) 3 g dK1 f f dK2 D 1 = K2+ 1- g, = K1-3 1- . (8) d3 3 R d3 + D f R (8) K1 K2 3 r + R, B-1(r + R) = 1, B = diag(b1, b2, b3). (9) B = (, B)-2, (10) ( M, B-1( M )) F2 =.

(, B) E = const F2 = const F2 = const F2 2 dK1 dK2 = - K2, = K1 - Q()U(z), d + D d (11) Q() dz = K2 d + D 2 2 K1 K2 1 H = + + U(z). (12) 2 + D ( + mR2) = mR2(, ) + MF, = R. (13) m v = I = E a R F MF MF U(x ) U MF = a x (x ) =, (14) |(x )| (x ) = (x, Bx ) - 2x3 = 0, B = diag(1/p, 1/q, 0) (15) 1(M H =, ) + U(x ) = h = const, (x ) = 0, (16) 2 4mg F = ( , B( ))|(x )|2 - (x, B2x ). (17) + mR2 1) p > 0 q > 0 2) pq < 0 3) p < 0 q < 0 22 > mg( + D)( |p| + |q|)2. (18) D1 = 0 m1u + + m2v = 0 |m1| + |m2| < 4 5 5 4 4 2 2 2 2 uvk2k1 3u2v2 -k2 - k1 + (k1 - k2)2 + 2k2k1 (u2 + v2)2 - v2u2 1 D1 =, 2 (u2 - v2)4 u v k1 k2 2 2 p = -k1, q = -k2, = , + D (19) 2 2 mg 22 k1 + k2 uv =, = u2 + v2 + uv.

+ D k1k2 ( + D)2 k1k2 E = 50 F = 20 p = 1 q = 10 m = 1 g = 1 D = 1 R = 0.1 1 1 x3 = (x, Bx) + (111x3 + 112x2x2 + 122x1x2 + 1 1 2 2 3 + 222x3) ijk i, j, k = 1, 2 2 (17) = M + m ( r) + mgr, (20) = .

M r g m M = I + + mr ( r) I = diag(I1, I2, I1) (r, B-1r) = 1 B = QT B0Q B0 = = diag(b2, b2, b2) 1 2 1 0 1 cos sin 0 bi Q =@ - sin cos 0A 0 0 1 r = B = p (, B) 1 H = (M, ) - mg(r, ), 2 (21) (, ) = 1.

= 0, (22) M + mgr = 0.

= (1, 0, 0) = (0, 1, 0) = (0, 0, 1) b2 > b1, I2 < I1, (23) sin2 < 0.

I = = diag(2.5, 0.5, 2.5) B0 = diag(1, 25, 1) m = 1 g = 980 = 0.08 E = 3000 = M + m ( r) + mgr , (24) = .

m r M M = I + mr ( r), (25) I = diag(I1, I2, I3) r R R1 Rr1 = -, r2 = -, r3 = 0. (26) 2 1 - 3 1 - 2 = 1 1(M H =, ) + U(), U = -mg(r, ) = mgR 1 - 3. (27) C1 C 2 = 2 sin2 (I1 + mR2)P (), 2 (28) K1 1 KP () = h - - - mgR sin , 2 I2I1 sin2 K1, K2 C1 C2 P () (28) H C1 C2 dP () P () = 0, = 0, (29) d C1 + + C2 = const C1 - C2 = const i = {Mi, H}, i = {i, H}, i = 1, 2, 3, (30) e(3) {Mi, Mj} = -ijkMk, {Mi, j} = -ijkk, {i, j} = 0, (31) 1(AM H =, M) - (r, ), (32) A = I-1 = diag(a1, a2, a3) (31) M, F1 = (M, ), F2 = 2. (33) 11 + 2 =. (34) 2 1 + r = 0 e Ox (r1 = 0, r2 = 0, r3 = 0) n = 1 n = 1 e1 e1, e2 e3 1. r3 = 0 (a2, a3) 2. r1 = 0 (a1, a2) I1 = I2 = 1 I3 = r = (0, , 0) < 2 0 1 = 23, 2 = -13, 3 = 1. (35) 2 2 2 2 1 + 2 = h, 11 + 22 = c, 1 + 2 + 3 = 1. (36) (35) (36) H H =, = -, (37) c2 H = + cos + 1 - sin( 2ht) sin .

c 2 2h 2h = 8.721...

h h c = 0 h = hmin = c2/2 (37) c = 0 h = h > 0 N mi, i = 1..N Rn i n ri pi H H i =, i = -, i = 1... N, pi ri (38) pi H = mi + U(|ri - rj|), H (38) E(n) Rn n(n - 1) n + (i) (i) P = pi, M = r p(i) - r p(i), (39) i (38) miri P c = R - t, R = (40) mi mi R (38) N Rn (39) n(n - 1) Q = RP - RP, , = 1... n. (41) P QP = 0, (42) <,,> = = = (41) (40) (38) M, P, Q R3 (39) (41) N R3 = -2 N p1 i H = (43) mi + U(r), i= U(r) U (44) (r, ) = U.

r (43) U(r) = U-2(r) + V (I) (45) J = 2I(H - V ) - (r, p)2. (46) (46) (45) (43) (45) mi d t = Id , qi = ri, q, r RN. (47) I (N - 1) (q, q) = U-q = - + q, (48) q e U- = (q, ) - q2 q qi U-2(q) = IU-2(r) = U-2( ), (49) mi (46) J = q2 + 2U-2(q), (50) (47) J S2 c1 c2 c1(M H = + M22 + M32) + + +. (51) 12 22 1(p c H = + p2 + p2) +. (52) 1 2 (x1x2x3)2/ N = -2 pi H = (53) mi + U-2(|ri - rj|).

(53) N R = = -2 N N P = pi, S = P (ri, pi) - 2H miri, i=1 i=(54) N M = ri pi, J = 2IH - ( (ri, pi))2.

i i= (38) N R3 = -2 (54) (53) aij U =. (55) (xi - xj)i

i=1 i>j (p + M)2 1 (p - M)1a1 H = p2 + + + + 2 2 cos2 cos2 sin2 2m2a+ + (58) m2 sin2 + 12 cos2 + m1 12 sin 2 cos 2m2a+, m2 sin2 + 12 cos2 - m2 12 sin 2 cos (m1 + m2)mm1m (0, ), [0, ), 1 =, 2 = 2 m1 + m2 m1 + m2 + m3 S2 S2 L U = - ctg (U = - cth ), (59) (59) S3 L3 S2 L p2 p1 1 2 J H = + + (c2 - (p1 + p2)2) + U(1 - 2).

2R2 m1 mm1m2 sin2(1 - 2) (60) p2 = 0 H = E 1, p1, 2 (60) (60) n (xi, yi) i H H ixi =, ii = -, 1 i n, (61) yi xi n H = - ij ln Mij, Mij = |ri - rj|2, ri = (xi, yi). (62) 4 i

n n n F1 = R i sin i cos i, F2 = R i sin i sin i, F3 = R i cos i.

i=1 i=1 i=(73) F (F1, F2, F3) = F = iri ri {Fi, Fj} = ijkFk. (74) R F3 F N FN = N = iri = 0 i= i, i i(F, ri+1 ri+2) i+i = |Fi+1|, tg i =, i = 1,..., N - 2, (ri+1 F, ri+2 F ) i+1 i+(75) N Fi = jrj i j=(Fi+1, ri+2) (Fi+1, ri+1) N FN = iri = 0 (70) i= (75) i = = 1,..., N - 1 = 2 = 3 = = -1 4 = 4 D = 3. (E, q2) = 8.721...

(t) ( T ) 1 a i(t);

2 a p 2 p, q Z) q T T a = 12(t)dt. (76) T p a 2 3 a o = ( = p, q T o q Z), 4 i(t) 2 3k (k)(E) = (0)(E) + 0(E), m N, k Z, (77) m m 2 3k m 0(E) = T (E) (k) mT m k (k)(E) = (0)(E) + 0(E), m, k Z, (78) 2m m 2 k m 0(E) = T T (E) 2mT (k)(E) = 0, (79) m k, m E N ik H = - ik ln tan2. (80) 4 i (86) h(D) 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24)

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