Plot multiple functions?

Questions
,
1

hi ,
when i tried to solve these eqns to give me function of anther variable …it gives me so many eqns and i cant know which the right ones so i couldnt plot them
i want to plot w3 , w4 with respect to varible theta2 (i want all varibles in output to be with respect to theta2}
i will attach the code programming

r1 = 600;
r2 = 200;
r3 = 700;
r4 = 900;
(* \[Theta]2 is NOT constant !..*)
\[Alpha]2 = 0;
\[Omega]2 = 12.568;

eq1 = -r1  + r2 Cos[\[Theta]2 ] + r3 Cos[\[Theta]3 ] + 
   r4 Cos[\[Theta]4 ] ;
eq2 = r2 Sin[\[Theta]2 ] + r3 Sin[\[Theta]3  ] + r4 Sin[\[Theta]4 ] ;
m = Map[{\[Theta]3 , \[Theta]4} /. # &, {ToRules[
      N[Reduce[{eq1 == 0 && eq2 == 0} , {\[Theta]3, \[Theta]4}] /. {C[
           1] -> 0 , C[2] -> 0}]]}]/Degree;
Plot[m, {\[Theta]2, 0, 2 Pi}]
eq3 = -r2 \[Omega]2 *Sin[\[Theta]2 Degree] - 
   r3 \[Omega]3 Sin[\[Theta]3 Degree] - 
   r4 \[Omega]4 Sin[\[Theta]4 Degree];
eq4 = r2 \[Omega]2 Cos[\[Theta]2 Degree] + 
   r3 \[Omega]3 Cos[\[Theta]3 Degree] + 
   r4 \[Omega]4 Cos[\[Theta]4 Degree];

q = Map[{\[Omega]3 , \[Omega]4} /. # &, {ToRules[
     N[Reduce[{eq3 == 0 && eq4 == 0} , {\[Omega]3 , \[Omega]4}]]]}];
Plot[q, {\[Theta]2, 0, 2 Pi}]
2

You seem to intend that q depends on \theta2 only. That is not the case

In[74]:= Variables[q]
Out[74]= {\[Omega]3, \[Omega]4, Cos[0.0174533 \[Theta]2], 
 Cos[0.0174533 \[Theta]3], Cos[0.0174533 \[Theta]4], 
 Csc[0.0174533 \[Theta]3], Csc[0.0174533 \[Theta]4], 
 Sec[0.0174533 \[Theta]3], Sec[0.0174533 \[Theta]4], 
 Sin[0.0174533 \[Theta]2], Sin[0.0174533 \[Theta]3], 
 Sin[0.0174533 \[Theta]4]}

and therefore the

Plot[q, {\[Theta]2, 0, 2 Pi}]

remains empty. You need to replace \theta3 and \theta4 by the results of the previous substitution.

What is the purpose of this calculation? To eliminate \theta3, \theta4, \omega3, \omega4, \alpha3, \alpha4 from the equations in order to get one expression in \theta2?

3

Why do only eq3 and eq4 have a Degree after the \theta2, \theta3, \theta4?

eq5 seems to have an error, it has three \theta3 and one \theta4 instead of two \theta3 and two \theta4 as eq6 has.

4

Does it mean something to you to look at it that way?

In[15]:= Clear[eq1, eq2, eq3, eq4, eq5, eq6]
eq1 = -r1 + r2 C2 + r3 C3 + r4 C4;
eq2 = r2 S2 + r3 S3 + r4 S4;
eq3 = -r2 \[Omega]2 S2 - r3 \[Omega]3 S3 - r4 \[Omega]4 S4;
eq4 = r2 \[Omega]2 C2 + r3 \[Omega]3 C3 + r4 \[Omega]4 C4;
eq5 = -r2 \[Alpha]2 S2 - r2 \[Omega]2^2 C2 - r3 \[Alpha]3 S3 - 
   r3 \[Omega]3^2 C3 - r4 \[Alpha]4 S4 - r4 \[Omega]4^2 C4;
eq6 = r2 \[Alpha]2 C2 - r2 \[Omega]2^2 S2 + r3 \[Alpha]3 C3 - 
   r3 \[Omega]3^2 S3 + r4 \[Alpha]4 C4 - r4 \[Omega]4^2 S4;

In[22]:= Reduce[{eq1 == 0, eq2 == 0, eq3 == 0, eq4 == 0, eq5 == 0, 
  eq6 == 0,
  S2^2 + C2^2 == 1, S3^2 + C3^2 == 1, S4^2 + C4^2 == 1}, {S3, C3, S4, 
  C4, \[Alpha]3, \[Alpha]4, \[Omega]3, \[Omega]4}]

During evaluation of In[22]:= Reduce::ratnz: Reduce was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result. >>

Out[22]= ((S2 == 0. - 1.33333 I || S2 == 0. + 1.33333 I) && 
   C2 == 1.66667 && S3 == 0.116071 S2 && C3 == -1.0119 && 
   S4 == -0.3125 S2 && 
   C4 == 1.08333 && \[Alpha]3 == 1285.89 S2 && \[Alpha]4 == 
    952.702 S2 && \[Omega]3 == 30.2418 && \[Omega]4 == 
    17.6738) || ((S2 == 0. - 2.82843 I || S2 == 0. + 2.82843 I) && 
   C2 == 3. && 
   S3 == -0.285714 S2 && (C3 == -1.28571 || C3 == 1.28571) && 
   S4 == 0 && 
   C4 == -0.777778 C3 && \[Alpha]3 == 
    2.19381 (27. S2 + 14. C3 S2) && \[Alpha]4 == 
    2.19381 (27. S2 + 14. C3 S2) && \[Omega]3 == 
    12.568 && \[Omega]4 == 
    0.465481 (27. + 14. C3)) || ((S2 == 0. - 3.69276 I || 
     S2 == 0. + 3.69276 I || S2 == 0. - 11.1294 I || 
     S2 == 0. + 11.1294 I) && 
   C2 == 0.0166667 (175. - 4. S2^2) && (S3 == 
      9.66557*10^-6 (-24780. S2 - 64. S2^3 - 
         1.41421 Sqrt[
          3.61694*10^9 + 3.21435*10^8 S2^2 + 1.58592*10^6 S2^4 + 
           2048. S2^6]) || 
     S3 == 9.66557*10^-6 (-24780. S2 - 64. S2^3 + 
         1.41421 Sqrt[
          3.61694*10^9 + 3.21435*10^8 S2^2 + 1.58592*10^6 S2^4 + 
           2048. S2^6])) && 
   C3 == 0.000352734 (11150. + 64. S2^2 - 3815. S2 S3 - 28. S2^3 S3) &&
    S4 == 0.111111 (-2. S2 - 7. S3) && 
   C4 == 0.000137174 (-22165. - 20. S2^2 + 7630. S2 S3 + 
       56. S2^3 S3) && \[Alpha]3 == 
    5.54249*10^-9 (1.36838*10^10 S2 + 1.06205*10^8 S2^3 + 
       3.94392*10^10 S3 + 3.02615*10^8 S2^2 S3) && \[Alpha]4 == 
    5.54249*10^-9 (1.20784*10^10 S2 + 9.59067*10^7 S2^3 + 
       3.25658*10^10 S3 + 2.63466*10^8 S2^2 S3) && \[Omega]3 == 
    0.000101192 (58075. + 260. S2^2 + 16100. S2 S3 + 
       112. S2^3 S3) && \[Omega]4 == -6.2464*10^-6 (-5.10267*10^6 - 
       24140. S2^2 + 1.11605*10^6 S2 S3 + 
       8624. S2^3 S3)) || ((C2 == -1. Sqrt[1. - 1. S2^2] || 
     C2 == Sqrt[1. - 1. S2^2]) && -5. + 3. C2 != 
    0 && (S3 == (
      0.0714286 (2. S2 - 6. C2 S2 - 
         4.24264 Sqrt[
          250. - 300. C2 + 90. C2^2 - 7. S2^2 + 3. C2 S2^2 + 
           2. C2^2 S2^2]))/(-5. + 3. C2) || 
     S3 == (0.0714286 (2. S2 - 6. C2 S2 + 
         4.24264 Sqrt[
          250. - 300. C2 + 90. C2^2 - 7. S2^2 + 3. C2 S2^2 + 
           2. C2^2 S2^2]))/(-5. + 3. C2)) && -3. + C2 != 0 && 
   C3 == (0.142857 (-2. + 6. C2 - 7. S2 S3))/(-3. + C2) && 
   S4 == 0.111111 (-2. S2 - 7. S3) && 
   C4 == 0.111111 (6. - 2. C2 - 7. C3) && -193750. + 182250. C2 + 
     66675. S2^2 + 2400. S2^4 + 16. S2^6 != 
    0 && \[Alpha]3 == -((2.92509 (1.84149*10^6 S2 - 476874. C2 S2 + 
           367416. C3 S2 + 21829. S2^3 + 26484. C2 S2^3 + 
           2772. S2^5 + 1.55925*10^6 S3 - 1.99395*10^6 C2 S3 - 
           763469. S2^2 S3 + 219324. C2 S2^2 S3 + 15372. S2^4 S3 - 
           289688. S2 S3^2))/(-193750. + 182250. C2 + 66675. S2^2 + 
         2400. S2^4 + 16. S2^6)) && \[Alpha]4 == 
    1.22885*10^-15 (2.24458*10^17 S2 - 1.29493*10^16 C2 S2 + 
       6.20893*10^16 C3 S2 + 5.59707*10^14 S2^3 + 
       2.25243*10^14 C2 S2^3 + 2.35755*10^13 S2^5 + 
       2.46529*10^16 S3 + 6.1083*10^16 C2 S3 - 
       8.49765*10^16 S2^2 S3 + 1.86532*10^15 C2 S2^2 S3 + 
       1.30737*10^14 S2^4 S3 - 2.84416*10^17 S2 S3^2 + 
       1.04667*10^15 \[Alpha]3 + 3.40562*10^14 S2^2 \[Alpha]3 + 
       7.71626*10^12 S2^4 \[Alpha]3 + 
       4.6521*10^10 S2^6 \[Alpha]3) && \[Omega]3 == 
    1.46664*10^-16 (-2.11516*10^17 - 1.46774*10^17 C2 - 
       4.01236*10^17 C3 + 3.56339*10^16 S2^2 - 
       1.36691*10^15 C2 S2^2 + 4.55857*10^14 S2^4 + 
       2.25308*10^14 C2 S2^4 + 2.35823*10^13 S2^6 + 
       1.1283*10^17 S2 S3 + 6.59829*10^15 C2 S2 S3 - 
       4.29285*10^15 S2^3 S3 + 1.86586*10^15 C2 S2^3 S3 + 
       1.30775*10^14 S2^5 S3 + 2.18653*10^17 S3^2 + 
       3.73233*10^14 S2 \[Alpha]3 + 3.07905*10^14 S2^3 \[Alpha]3 + 
       7.51326*10^12 S2^5 \[Alpha]3 + 
       4.65345*10^10 S2^7 \[Alpha]3) && \[Omega]4 == 
    3.99252*10^-15 (-6.13054*10^15 - 3.9879*10^15 C2 - 
       9.82606*10^15 C3 + 1.04034*10^15 S2^2 - 
       4.19126*10^13 C2 S2^2 + 1.28147*10^13 S2^4 + 
       6.471*10^12 C2 S2^4 + 6.773*10^11 S2^6 + 3.40531*10^15 S2 S3 + 
       1.67527*10^14 C2 S2 S3 - 1.24834*10^14 S2^3 S3 + 
       5.35888*10^13 C2 S2^3 S3 + 3.75593*10^12 S2^5 S3 + 
       6.24702*10^15 S3^2 + 1.06647*10^13 S2 \[Alpha]3 + 
       8.79869*10^12 S2^3 \[Alpha]3 + 2.15237*10^11 S2^5 \[Alpha]3 + 
       1.3365*10^9 S2^7 \[Alpha]3))
5

With \omega2=\frac{1571}{125} the Reduce[] runs without warnings, giving at least a starting point for further work.