Double Pendulum Studies

[MasterGy]

My God! :))  Fill your pdf with amazement!(translation error? amazes me) Unfortunately, I do not understand the interpretation of advanced algebra. I can’t wait to see the movement of N arms on the screen work. In the meantime, I’m also wondering how this could be easiest. Good luck, I hope we can see the program work as soon as possible !!!

[STxAxTIC]

By the way - there is a completely different approach to doing rigid body motion.

https://qb64forum.alephc.xyz/index.php?topic=3837.msg131887#msg131887

It uses a bunch of matrix algebra but a Newtonian method, not a Lagrangian one. Pretty good stuff though.

[STxAxTIC]

REDACTED

[Pete]

Ah, hold on there sparky, the "Press any key for next case." is broken. Any key pressed results in an exit. Now the first example works as expected. The modification to the effect, however, is quite impressive. This is probably just a small glitch in the transformation process. Wish I could understand the math. It's a bit over my head, but it sure feels nice.

Pete

[MasterGy]

I still didn’t delve into the math part. works fantastic with 3 wrists! Will I need to write a control for N joints separately? one for each?

[MasterGy]

I was thinking of a different approach. The way you calculate it is too complicated for me. I was wondering what if the masses only had a vector. No other. Strength and direction. An inertia. How that would change would determine what it connects to. The distances need to be somewhat flexible, so you don’t necessarily have to calculate with just one huge calculation who is exactly where. For now, it works with these values. I try to take the elasticity as low as possible, the length of the ropes will always be fixed (apparently). This will have the effect of being like a pendulum like yours.

Obj_c is the number of bullets. The obj array contains the position, vector.
The conn array contains the connections. For example.
conn (x, 0) index obj connected to conn (x, 1) obj, rope of conn (x, 2) length

Code: QB64: [Select]

1. RANDOMIZE TIMER
2. CONST pip180 = 3.141592 / 180
3. monx = 800: mony = 600: mon = _NEWIMAGE(monx, mony, 32): SCREEN mon
4.  
5. gravity = 1
6. obj_c = 10 'number objects
7. DIM obj(obj_c - 1, 9) '0,1 posX,Y 3fix/mover
8. rad = 10 'circle rad
9.  
10.  
11. cent_x = monx / 2: cent_y = 20: zoom = .05
12.  
13.  
14. 'objects location
15. FOR a = 1 TO obj_c - 1
16.     obj(a, 0) = (RND(1) - .5) * 10000
17.     obj(a, 1) = (RND(1) - .5) * 5000
18.     obj(a, 3) = 1 '<---- 0 if fix, 1 if fly
19. NEXT a
20.  
21. 'connections
22. conn_c = obj_c - 1: DIM conn(conn_c - 1, 2)
23. FOR a = 0 TO conn_c - 1
24.     conn(a, 0) = a: conn(a, 1) = a + 1
25.     conn(a, 2) = 30 'rope width
26. NEXT a
27.  
28.  
29. DO: _LIMIT 100: IF INKEY$ = CHR$(27) THEN END
30.     'draw objects
31.     FOR a = 0 TO obj_c - 1
32.         x = cent_x + obj(a, 0) * zoom
33.         y = cent_y + obj(a, 1) * zoom
34.         IF mouse_near = a THEN COLOR _RGB32(255, 0, 0) ELSE COLOR _RGB32(200, 200, 200)
35.         CIRCLE (x, y), rad
36.         _PRINTSTRING (x, y), LTRIM$(STR$(a))
37.     NEXT a
38.  
39.     'draw connections
40.     COLOR _RGB32(150, 150, 150)
41.     FOR a = 0 TO conn_c - 1:
42.         x1 = obj(conn(a, 0), 0) * zoom + cent_x
43.         y1 = obj(conn(a, 0), 1) * zoom + cent_y
44.         x2 = obj(conn(a, 1), 0) * zoom + cent_x
45.         y2 = obj(conn(a, 1), 1) * zoom + cent_y
46.     LINE (x1, y1)-(x2, y2): NEXT a
47.  
48.     'calculate moving
49.     FOR a = 0 TO obj_c - 1: IF obj(a, 3) = 0 OR (mouse_near = a AND _MOUSEBUTTON(1)) THEN _CONTINUE
50.  
51.         'connections vector
52.         vec_x = 0: vec_y = 0: vec_c = 0
53.         FOR t = 0 TO conn_c - 1: x = -1: FOR t2 = 0 TO 1: IF conn(t, t2) = a THEN x = conn(t, t2 XOR 1)
54.             NEXT t2
55.             IF x <> -1 THEN
56.                 disx = obj(a, 0) - obj(x, 0)
57.                 disy = obj(a, 1) - obj(x, 1)
58.                 ang = (-degree(disx, disy) + 0) * pip180
59.                 dis = SQR(disx * disx + disy * disy)
60.                 power = ABS(dis - conn(t, 2)) / 70
61.                 vec_x = vec_x + SIN(ang) * power
62.                 vec_y = vec_y - COS(ang) * power
63.                 vec_c = vec_c + 1
64.             END IF
65.         NEXT t
66.  
67.         obj(a, 4) = (obj(a, 4) + vec_x / vec_c) * .99
68.         obj(a, 5) = (obj(a, 5) + vec_y / vec_c + gravity) * .99
69.         obj(a, 0) = obj(a, 0) + obj(a, 4)
70.         obj(a, 1) = obj(a, 1) + obj(a, 5)
71.  
72.     NEXT a
73.  
74.     WHILE _MOUSEINPUT: WEND
75.  
76.     'mouse moving activing
77.     IF moving = 0 THEN
78.         mouse_near = -1
79.         FOR a = 0 TO obj_c - 1
80.             disx = (cent_x + obj(a, 0) * zoom) - _MOUSEX
81.             disy = (cent_y + obj(a, 1) * zoom) - _MOUSEY
82.             dis = SQR(disx * disx + disy * disy)
83.             IF dis < 10 THEN mouse_near = a
84.         NEXT a
85.     END IF
86.  
87.     IF (_MOUSEBUTTON(1) AND mouse_near <> -1) OR moving THEN
88.         moving = 1
89.         obj(mouse_near, 0) = (_MOUSEX - cent_x) / zoom
90.         obj(mouse_near, 1) = (_MOUSEY - cent_y) / zoom
91.     END IF
92.  
93.     moving = moving AND _MOUSEBUTTON(1)
94.  
95.     LOCATE 1, 1: PRINT "grab the ball with the mouse and move it!"
96.     _DISPLAY: CLS
97.  
98. LOOP
99.  
100.  
101.  
102.  
103. FUNCTION degree (a, b): degreex = ATN(a / (b + .00001)) / pip180: degreex = degreex - 180 * ABS(0 > b): degreex = degreex - 360 * (degreex < 0): degree = degreex: END FUNCTION
104.  

[STxAxTIC]

REDACTED

[Pete]

Both of these last two code examples are great, but totally unrealistic. You guys are missing the Tangle Effect. This is a law of physics that states any string in motion eventually ends up as a knot. Yep, you guessed it. Pete's knot happy!

Maybe we need a computer simulation board. These are, kidding aside, very cool!

Pete

[MasterGy]

I would like to present the work of STxAxTIC. Man starts and something moves relative to something. the clock arms can be described in a few lines.

mon = _NEWIMAGE(600, 600, 32): SCREEN mon
r(0) = 12: r(1) = 60: r(2) = 60: r(3) = 100
DO
    t$ = TIME$ + ":" + RIGHT$("00" + LTRIM$(STR$(TIMER)), 2)
    x1 = _WIDTH(mon) / 2: y1 = _HEIGHT(mon) / 2
    FOR t = 0 TO 3
        ang = 360 / r(t) * VAL(MID$(t$, t * 3 + 1, 2)) * (3.141592 / 180)
        rad = (4 - t) ^ 1 * (_WIDTH(mon) * .05)
        x2 = SIN(ang) * rad + x1
        y2 = -COS(ang) * rad + y1
        LINE (x1, y1)-(x2, y2)
        x1 = x2
        y1 = y2
    NEXT t

    _DISPLAY
    CLS
LOOP





  Or something like this. Could be clarified, it is irrelevant now. I am writing an example to Bplus that there are two things here!
STxAxTIC was brave and climbed into the most cruel pots of physics. I was wondering if it could be simplified. I tried, but those results didn't come out. This cannot be achieved by "cheap" means.
  Congratulations to STxAxTIC for his patience and fanaticism for showing a great connection without neglecting the rigor of physics! Congratulations!

[bplus]

STxAxTIC was brave and climbed into the most cruel pots of physics.

Yeah I think he might be stuck in there ;-))

Code: QB64: [Select]

1. mon = _NewImage(600, 600, 32): Screen mon
2. r(0) = 12: r(1) = 60: r(2) = 60: r(3) = 100
3. Do
4.     t$ = Time$ + ":" + Right$("00" + LTrim$(Str$(Timer)), 2)
5.     x1 = _Width(mon) / 2: y1 = _Height(mon) / 2
6.     For t = 0 To 3
7.         ang = 360 / r(t) * Val(Mid$(t$, t * 3 + 1, 2)) * (3.141592 / 180)
8.         rad = (4 - t) ^ 1 * (_Width(mon) * .05)
9.         x2 = Sin(ang) * rad + x1
10.         y2 = -Cos(ang) * rad + y1
11.         drawPully -1, x1, y1, .1 * rad, x2, y2, .1 * (4 - (t + 1)) ^ 1 * (_Width(mon) * .05), _RGB32(255 - t * 64)
12.         x1 = x2
13.         y1 = y2
14.     Next t
15.     _Display
16.     Cls
17. Loop
18.  
19. Sub drawPully (withCircles, x1, y1, r1, x2, y2, r2, c As _Unsigned Long)
20.     Dim a, a1, a2, x3, x4, x5, x6, y3, y4, y5, y6
21.     a = _Atan2(y2 - y1, x2 - x1)
22.     a1 = a + _Pi(1 / 2)
23.     a2 = a - _Pi(1 / 2)
24.     x3 = x1 + r1 * Cos(a1): y3 = y1 + r1 * Sin(a1)
25.     x4 = x1 + r1 * Cos(a2): y4 = y1 + r1 * Sin(a2)
26.     x5 = x2 + r2 * Cos(a1): y5 = y2 + r2 * Sin(a1)
27.     x6 = x2 + r2 * Cos(a2): y6 = y2 + r2 * Sin(a2)
28.     Line (x3, y3)-(x5, y5), c
29.     Line (x4, y4)-(x6, y6), c
30.     If withCircles Then
31.         Circle (x1, y1), r1, c
32.         Circle (x2, y2), r2, c
33.     End If
34. End Sub
35.  
36.  
37.  

Something wrong with 4th arm :(

[MasterGy]

Bplus, the "drawpully" is a very excellent SUB !!! :)

[Pete]

If only we had QB64 for the iwatch! Oh well, I think I'll wait for the digital version.

Pete

[STxAxTIC]

REDACTED