# Manipulate not moving when combining with ListPlot

I am trying to plot an interactive graph of the geometry about grid-transformation of Lorentz transformation by varying the velocity v. I was successful to draw the stationary graph, but the animation didn't move, and it was freezed at the initial condition v=0.7. If I removed the initial condition, the graph will have no lines.

How can I get it fixed? Many thanks!

v=0.7
\[Alpha]=Sqrt[1-v^2]
L={{1/\[Alpha],-v/\[Alpha]},{-v/\[Alpha],1/\[Alpha]}}
f[T_: List,x_: List]:=T.x
myinput=DeleteDuplicates@Flatten[Union[Table[{i,j},{i,0,3,1},{j,0,5,.01}],Table[{i,j},{i,0,3,.011},{j,0,5,1}]],1];
ListPlot[myinput]
ListPlot[f[L,#]&/@myinput]
Manipulate[ListPlot[f[L,#]&/@myinput],{v,0,1}]

• use L[v_] := {{1/\[Alpha], -v/\[Alpha]}, {-v/\[Alpha], 1/\[Alpha]} and Manipulate[ListPlot[f[L[v], #] & /@ myinput], {v, 0, 1}] ? – egwene sedai Apr 12 '18 at 20:07
• Thanks. I just tried, but then the grid/lines will disappear. Even for the stationary plot, there will be no grid. – H42 Apr 12 '18 at 20:15
• you need to remove the old definition of L; either restart mathematica or by ClearAll[L]; L[v_] := {{1/\[Alpha], -v/\[Alpha]}, {-v/\[Alpha], 1/\[Alpha]}} – egwene sedai Apr 12 '18 at 20:19
• Thanks! Finally got it solved. changed \[Alpha] to \[Alpha][v_] as well – H42 Apr 13 '18 at 0:45