Double Pendulum

An implementation of a double pendulum

Author: aefarrell

art/pendulum/pendulum.bas

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+/*
+  Double Pendulum
+
+A double pendulum implementation, uses 
+RK4 to integrate each time step, which 
+requires that the user have loaded 
+rk4.bas into the library using 
+LIBRARY SAVE prior to running this.
+
+The initial conditions and system
+parameters start after the function
+and subroutine definitions.
+
+*/
+
+option angle radians
+option base 1
+framebuffer create
+framebuffer write f
+cls rgb(black)
+
+'system of equations dy/dt=rhs(t,y)
+function rhs(t,y(),dy()) as integer
+ local float o1=y(1) '\theta_1
+ local float w1=y(2) '\omega_1
+ local float o2=y(3) '\theta_2
+ local float w2=y(4) '\omega_2
+
+ local float del=o2-o1
+ local float den=(m1+m2)-m2*cos(del)^2
+ dy(1)=y(2) '\dot{\theta_1} = \omega_1
+ dy(2)=((m2*l1*w1^2)*sin(del)*cos(del)+ m2*g*sin(o2)*cos(del)+ m2*l2*w2^2*sin(del)- (m1+m2)*g*sin(o1))/(l1*den)
+ dy(3)=y(4)
+ dy(4)=(-m2*l2*w2^2*sin(del)*cos(del)+ (m1+m2)*(g*sin(o1)*cos(del)- l1*w1^2*sin(del) - g*sin(o2)))/(l2*den)
+
+ rhs = 1
+end function
+
+sub plot_pen x1,y1,x2,y2
+ static integer h  = MM.VRES
+ static integer w  = MM.HRES
+ static integer xo = w\2
+ static integer yo = h\2
+ static float scl = h/2/(l1+l2)
+ static float rad = 10/(m1+m2)
+ static integer r1 = fix(m1*rad)
+ static integer r2 = fix(m2*rad)
+ local integer px1 = fix(x1*scl)+xo
+ local integer py1 = yo-fix(y1*scl)
+ local integer px2 = fix(x2*scl)+xo
+ local integer py2 = yo-fix(y2*scl)
+
+ cls rgb(black)
+ line xo,yo,px1,py1,1,rgb(green)
+ circle px1,py1,r1,1,,rgb(blue),-1
+ line px1,py1,px2,py2,1,rgb(green)
+ circle px2,py2,r2,1,,rgb(blue),-1
+ framebuffer copy f,n
+end sub
+
+'system parameters
+dim float g  = 9.81'm/s^2
+dim float l1 = 1.0 'm
+dim float m1 = 1.0 'kg
+dim float l2 = 1.0 'm
+dim float m2 = 1.0 'kg
+
+'initial conditions and integration
+dim float dt=0.05
+dim float y(4) = (pi/2,0,pi/2,0)
+dim float th1,th2,x1,y1,x2,y2
+dim integer f,i
+do
+ f   = rk4step("rhs",y(),0,dt)
+ th1 = y(1)
+ x1  = l1*sin(th1)
+ y1  = -l1*cos(th1)
+ th2 = y(3)
+ x2  = x1+l2*sin(th2)
+ y2  = y1-l2*cos(th2)
+ plot_pen x1,y1,x2,y2
+loop

art/pendulum/pendulum.bmp

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+title: Double Pendulum 
+date: 2025-12-15
+program: pendulum.bas
+screenshot: pendulum.bmp
+description: A simulation of a chaotic pendulum. The system of equations and the plotting subroutine are generic enough that the mass of the pendulums and the lengths of the pendulum arms can be adjusted and everything will be scaled to fit within the screen dimensions. The pendulum is anchored at the center of the screen and simply plays out forever (until the user hits break). Requires that the RK-4 routine in rk4.bas be loaded into the library.