<< Graphics`Animation`

u  = 1
v  = 1
k  =  .6
a  = 1
Sp  = 1
Jin  = 1
ℏ = 1
pts2 = Point[{0, 0, 0}]
pts3 = Point[{0, -0, 0}]
pts4 = Point[{-0, 0, 0}]
pts5 = Point[{-0, -0, 0}]
Solucion = 
      DSolve[{(u/v) x'[
                t] == ((Sp 2 Jin)/ℏ) (2 y[
                      t] - (Cos[k a] y[t] + Cos[k a] y[t])), 
          (v/u) y'[
                t] == ((-Sp 2 Jin)/ℏ) (2 x[
                      t] - (Cos[k a] x[t] + Cos[k a] x[t])), 
          x[0] == Cos[0 k a], y[0] == Cos[0 k a]}, {x[t], 
          y[t]}, t]
wotan[t_] := x[t] /.  Solucion[[1, 1]]
h[t_] := t + 2
g[t_] := Composition[wotan, h]
sigfried[t_] := 
      y[t] /. Solucion[[1, 
            2]]

Plot[
      Evaluate[x[t] /.  Solucion[[1, 1]]], {t, 0, 
        20}]
Plot[
      Evaluate[y[t] /.  Solucion[[1, 2]]], {t, 0, 
        20}]
linea2 = 
        Line[{{0, 0, 0}, {wotan[t] /. t -> t + 0, sigfried[t], 
              2}}];
linea4 = 
        Line[{{0, 2, 0}, {wotan[t] /. t -> t + (1 k a ) , 
              2 + sigfried[t] /. t -> t + (1 k a) , 
              2}}];
linea5 = 
        Line[{{0, 4, 0}, {wotan[t] /. t -> t + (2 k a ) , 
              4 + sigfried[t] /. t -> t +  (2 k a), 
              2}}];
linea6 = 
        Line[{{0, 6, 0}, {wotan[t] /. t -> t + (3 k a) , 
              6 + sigfried[t] /. t -> t + (3 k a) , 
              2}}];
linea7 = 
        Line[{{0, 8, 0}, {wotan[t] /. t -> t + (4 k a ) , 
              8 + sigfried[t] /. t -> t +  (4 k a), 
              2}}];
linea8 = 
        Line[{{0, 10, 0}, {wotan[t] /. t -> t + (5 k a ) , 
              10 + sigfried[t] /. t -> t +  (5 k a), 
              2}}];
linea9 = 
        Line[{{0, 12, 0}, {wotan[t] /. t -> t + (6 k a) , 
              12 + sigfried[t] /. t -> t + (6 k a) , 
              2}}];
linea10 = 
        Line[{{0, 14, 0}, {wotan[t] /. t -> t + (7 k a ) , 
              14 + sigfried[t] /. t -> t +  (7 k a), 
              2}}];
linea11 = 
        Line[{{0, 16, 0}, {wotan[t] /. t -> t + (8 k a ) , 
              16 + sigfried[t] /. t -> t +  (8 k a), 
              2}}];
linea12 = 
        Line[{{0, 18, 0}, {wotan[t] /. t -> t + (9 k a) , 
              18 + sigfried[t] /. t -> t + (9 k a) , 
              2}}];
linea13 = 
        Line[{{0, 20, 0}, {wotan[t] /. t -> t + (10 k a ) , 
              20 + sigfried[t] /. t -> t +  (10 k a), 
              2}}];
linea14 = 
        Line[{{0, 22, 0}, {wotan[t] /. t -> t + (12 k a) , 
              22 + sigfried[t] /. t -> t + (12 k a) , 
              2}}];
linea15 = 
        Line[{{0, 24, 0}, {wotan[t] /. t -> t + (14 k a ) , 
              24 + sigfried[t] /. t -> t +  (14 k a), 
              2}}];
linea16 = 
        Line[{{0, 26, 0}, {wotan[t] /. t -> t + (16 k a ) , 
              26 + sigfried[t] /. t -> t +  (16 k a), 
              2}}];
linea17 = 
        Line[{{0, 28, 0}, {wotan[t] /. t -> t + (18 k a) , 
              28 + sigfried[t] /. t -> t + (18 k a) , 
              2}}];
linea18 = 
        Line[{{0, 30, 0}, {wotan[t] /. t -> t + (20 k a ) , 
              30 + sigfried[t] /. t -> t +  (20 k a), 
              2}}];
Table[
        Graphics3D[{AbsoluteThickness[2], linea2, linea4, linea5, linea6,  
            linea7, linea8,  linea9,  linea10, linea11,  linea12,  
            linea13, linea14, linea15, linea16, linea17, linea18, pts2, pts3, 
            pts4, pts5}, PlotRange -> {0, 3}, Axes -> True, 
          BoxRatios -> {3, 30, 3}], {t, 0, 70}] // 
      Short
ShowAnimation[%]

u  = 1
v  = 1
k  = 1
a  = 1
Sp  = 1
Jin  = 1
ℏ = 1