I have two equation for Ex(t1,t2,t)
and Ey(t1,t2,t)
. Please,could you tell me, how I can make a plot Ex(Ey)
?
Ex[t1_, t2_, t_] = ((Sin[t2] - Sin[t1])/(t1 - t2) - Cos[t])^2
Ey[t1_, t2_, t_] = (2 (Cos[t1] - Cos[t2])/(t1 - t2) - Sin[t])^2
I have two equation for Ex(t1,t2,t)
and Ey(t1,t2,t)
. Please,could you tell me, how I can make a plot Ex(Ey)
?
Ex[t1_, t2_, t_] = ((Sin[t2] - Sin[t1])/(t1 - t2) - Cos[t])^2
Ey[t1_, t2_, t_] = (2 (Cos[t1] - Cos[t2])/(t1 - t2) - Sin[t])^2
What you really have is a family of parametric curves. I would go about doing this in the following way (and you can switch out t
for t1
or t2
if you want; just follow the general construction).
As an example, consider:
With[{t1 = 0.5, t2 = 0},
ParametricPlot[{Ey[t1, t2, t], Ex[t1, t2, t]}, {t, 0, 2 π}, AspectRatio -> 1]
]
If you want to see some general behavior, we can make a table over one of the other variables. For instance,
Multicolumn[
Table[
With[{t2 = 0}, ParametricPlot[{Ey[t1, t2, t], Ex[t1, t2, t]}, {t, 0, 2 π}, AspectRatio -> 1]],
{t1, {0.01, 0.1, 0.5, 1, 2, 5}}],
3]
If you are not after a continuous solution, then this is straightforward:
min = 0.;
max = 2.;
step = 0.1;
ListPlot[
Transpose@{Flatten@
Quiet@Table[
Ey[x, y, z], {x, min, max, step}, {y, min, max, step}, {z, min,
max, step}],
Flatten@Quiet@
Table[Ex[x, y, z], {x, min, max, step}, {y, min, max, step}, {z,
min, max, step}]}, Frame -> True, AspectRatio -> 1,
FrameLabel -> {"Ey", "Ex"}]
Explanation: for a set {x,y,z}
the functions Ex[x,y,z]
and Ey[x,y,z]
take some values, say, E1
and E2
, respectively. So for sure when the function Ex
takes the value E1
, then function Ey
takes the value E2
. So one needs to make a list of such pairs {E2, E1}
. Quiet
is because when the denominator (t1-t2
in the definitions) is zero, then both functions are Indeterminate
, and I didn't want to play around with discarding such values as they don't influence the plot.