#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Aug 16 11:59:37 2021 @author: yz3259 """ import tkinter as tk import numpy as np import time from scipy.integrate import odeint w = 1400//2.5 h = 1200//2.5 r1 = 80 r2 = 80 m1 = 10 m2 = 5 xf, yf = (w//2, 500//3.2) A1, A2 = (95.0,-30.0) v1 = 0 v2 = 0 a1 = 0 a2 = 0 g = 10.0 flag = False def create_circle(x, y, r, canvasName,col = "black"): #center coordinates, radius x0 = x - r y0 = y - r x1 = x + r y1 = y + r return canvasName.create_oval(x0, y0, x1, y1,fill=col,outline=col) # def dA_dt(A): # ang1, ang2,v1,v2,a1,a2 = A # num1 = -g*(2*m1+m2)*np.sin(ang1) # num2 = -m2*g*np.sin(ang1-2*ang2) # num3 = -2*np.sin(ang1-ang2)*m2 # num4 = v2**2*r2+v1**2*r1*np.cos(ang1-ang2) # den = r1*(2*m1+m2-m2*np.cos(2*ang1-2*ang2)) # a1 = (num1+num2+num3*num4)/den # num1 = 2*np.sin(ang1-ang2) # num2 = v1**2*r1*(m1+m2) # num3 = g*(m1+m2)*np.cos(ang1) # num4 = v2**2*r2*m2*np.cos(ang1-ang2) # den = r2*(2*m1+m2-m2*np.cos(2*ang1-2*ang2)) # a2 = num1*(num2+num3+num4)/den # print(a1) # print(a2) # return np.array([ang1,ang2, v1,v2,a1,a2]) def funt(y): ang1 = y[0] ang2 = y[1] v1 = y[2] v2 = y[3] num1 = -g*(2*m1+m2)*np.sin(ang1) num2 = -m2*g*np.sin(ang1-2*ang2) num3 = -2*np.sin(ang1-ang2)*m2 num4 = v2**2*r2+v1**2*r1*np.cos(ang1-ang2) den = r1*(2*m1+m2-m2*np.cos(2*ang1-2*ang2)) a1 = (num1+num2+num3*num4)/den num1 = 2*np.sin(ang1-ang2) num2 = v1**2*r1*(m1+m2) num3 = g*(m1+m2)*np.cos(ang1) num4 = v2**2*r2*m2*np.cos(ang1-ang2) den = r2*(2*m1+m2-m2*np.cos(2*ang1-2*ang2)) a2 = num1*(num2+num3+num4)/den dydt = np.zeros(4) dydt[0] = v1 dydt[1] = v2 dydt[2] = a1 dydt[3] = a2 return dydt def rk4(A,h): # print(x0.shape) #print(A.shape) k1 = funt(A) k2 = funt(A+h*k1/2) k3 = funt(A+h*k2/2) k4 = funt(A+h*k3) y1 = A + h*(k1+2*k2+2*k3+k4)/6 #x0,A = t1,y1 return y1 # def rk4(x,y,h): # k1 = funt(x,y) # x1 = x+ k1[0]*h/2 # y1 = y + k1[1]*h/2 # k2 = funt(x1,y1) # x2 = x1+ k2[0]*h/2 # y2 = y1 + k2[1]*h/2 # k3 = funt(x2, y2) # x3 = x2+ k3[0]*h # y3 = y2 + k3[1]*h # k4 = funt(x3,y3) # return [x+h*(k1[0]+k2[0]*2+k3[0]*2+k4[0])/6,y+h*(k1[1]+k2[1]*2+k3[1]*2+k4[1])/6] root = tk.Tk() root.title("Double Pendulum") root.geometry("1200x1200") choice = tk.Frame(root,width = 1000//3, height = 1000//3, bd = 0,bg = "ivory") choice.grid(row=0,column = 0,padx = 5, pady =5) graph = tk.Frame(root,width = 1000//3, height = 1200//3, bd = 0) graph.grid(row=0,column = 1,padx=5,pady = 5) #graph2 = tk.Frame(root,width = 1000, height = 1000,bd=0) #graph2.grid(row=1,column=0,padx = 25, pady = 10) labe1 = tk.Label(graph, text = "Double Pendulum Movement",font = ('arial', 14, 'bold')).grid(row=0,column=0) my_canvas = tk.Canvas(graph,width =w, height =h+10, bg = "ivory") my_canvas.grid(row=1,column=0,padx = 5,pady=5) labe2 = tk.Label(graph, text = "Pendulum 1- angle and angular velocity",font = ('arial', 14, 'bold')).grid(row=2,column=0) track_canvas = tk.Canvas(graph,width =w, height = h//2-20, bg = "ivory") track_canvas.grid(row=3,column=0,padx=5,pady=5) #labe2 = tk.Label(graph2, text = "Pendulum 2- angle and angular velocity",font = ('arial', 14, 'bold')).grid(row=4,column=0) #track_canvas2 = tk.Canvas(graph2,width =w, height = h//2-20, bg = "ivory") #track_canvas2.grid(row=0,column=0,padx=20,pady=10) #flag = False def slide(): global line1,line2,circle1,circle2 #my_label = tk.Label(choice,text=angle1.get()) #my_label.grid(row=6,column=1) A1 = angle1.get() A2 = angle2.get() m1 = mass1.get() m2 = mass2.get() r1 = rod1.get() r2 = rod2.get() v1 = 0 v2 = 0 a1 = 0 a2 = 0 g = 10.0 ang1 = np.pi*A1/180 ang2 = np.pi*A2/180 t = 0 A = np.array([ang1,ang2,v1,v2]) track_canvas.delete("all") my_canvas.delete("all") flag = True while flag: # num1 = -g*(2*m1+m2)*np.sin(ang1) # num2 = -m2*g*np.sin(ang1-2*ang2) # num3 = -2*np.sin(ang1-ang2)*m2 # num4 = v2**2*r2+v1**2*r1*np.cos(ang1-ang2) # den = r1*(2*m1+m2-m2*np.cos(2*ang1-2*ang2)) # a1 = (num1+num2+num3*num4)/den # num1 = 2*np.sin(ang1-ang2) # num2 = v1**2*r1*(m1+m2) # num3 = g*(m1+m2)*np.cos(ang1) # num4 = v2**2*r2*m2*np.cos(ang1-ang2) # den = r2*(2*m1+m2-m2*np.cos(2*ang1-2*ang2)) # a2 = num1*(num2+num3+num4)/den # print(V) x1 = r1*np.sin(A[0])+ xf y1 = r1*np.cos(A[0]) + yf x2 = x1+r2*np.sin(A[1]) y2 = y1+r2*np.cos(A[1]) # Create line # my_canvas.delete("all") my_canvas.delete(line1,line2,circle1,circle2) line1 = my_canvas.create_line(xf,yf,x1,y1,fill = "black",width=4) circle1 = create_circle(x1,y1,m1,my_canvas,col = "black") # second pendulum line2 = my_canvas.create_line(x1,y1,x2,y2,fill = "black",width = 4) circle2 = create_circle(x2,y2,m2,my_canvas,col = "black") create_circle(x2,y2,1,my_canvas,col="skyblue") # v1 += a1 # v2 += a2 # ang1 += v1 # ang2 += v2 # v1 *=0.999 # v2 *=0.999 #my_canvas.delete(line1,line2,circle1,circle2) create_circle(t,180.0*(A[0])/np.pi+ h//4-10,1,track_canvas,col="gray") create_circle(t,180.0*A[2]/np.pi+h//4-10,1,track_canvas,col="coral") # create_circle(t,180.0*(ang1)/np.pi+ h//4-10,2,track_canvas2,col="gray") # create_circle(t,180.0*v1/np.pi+h//4-10,2,track_canvas2,col="coral") #print(v1) step = 0.1 t += step #print(t) A = rk4(A,step) #A[2] = A[2]*0.9991 #A[3] = A[3]*0.9991 root.update() # time.sleep(0.01) return # flag = True length_label = tk.Label(choice, text="Angle 1",font = ('arial', 14, 'bold')).grid(row=0, column=0, pady=5, padx = 5) angle1 = tk.Scale(choice,from_=-360, to =360,font = ('arial', 14, 'bold'),tickinterval= 180,orient = tk.HORIZONTAL,width = 20,length = 200) angle1.set(A1) angle1.grid(row=0,column=1,columnspan=10,padx = 5,pady=5) length_label = tk.Label(choice, text="Angle 2",font = ('arial', 14, 'bold')).grid(row=1, column=0, pady=5, padx = 5) angle2 = tk.Scale(choice, from_=-360, to =360,font = ('arial', 14, 'bold'),tickinterval= 180,orient = tk.HORIZONTAL,width = 20,length = 200) angle2.set(A2) angle2.grid(row=1,column=1,columnspan=10,padx = 5,pady=5) mass_label = tk.Label(choice, text="Mass 1",font = ('arial', 14, 'bold')).grid(row=2, column=0, pady=5, padx = 5) mass1 = tk.Scale(choice, from_=0, to =200,font = ('arial', 14, 'bold'),tickinterval= 50,orient = tk.HORIZONTAL,width = 20,length = 200) mass1.set(m1) mass1.grid(row=2,column=1,columnspan=100,padx = 5,pady=5) mass_label = tk.Label(choice, text="Mass 2",font = ('arial', 14, 'bold')).grid(row=3, column=0, pady=5, padx = 5) mass2 = tk.Scale(choice, from_=0, to =100,font = ('arial', 14, 'bold'),tickinterval= 50,orient = tk.HORIZONTAL,width = 20,length = 200) mass2.set(m2) mass2.grid(row=3,column=1,columnspan=10,padx = 5,pady=5) string_label = tk.Label(choice, text="Rod 1 Length",font = ('arial', 14, 'bold')).grid(row=4, column=0, pady=5, padx = 5) rod1 = tk.Scale(choice, from_=0, to =200,font = ('arial', 14, 'bold'),tickinterval= 200,orient = tk.HORIZONTAL,width = 20,length = 200) rod1.set(r1) rod1.grid(row=4,column=1,columnspan=10,padx = 5,pady=5) string_label = tk.Label(choice, text="Rod 2 Length",font = ('arial', 14, 'bold')).grid(row=5, column=0, pady=5, padx = 5) rod2 = tk.Scale(choice, from_=0, to =200,font = ('arial', 14, 'bold'),tickinterval= 200,orient = tk.HORIZONTAL,width = 20,length = 200) rod2.set(r2) rod2.grid(row=5,column=1,columnspan=10,padx = 5,pady=5) my_btn = tk.Button(choice,text="Start", command = slide,padx=10,pady=20,font = ('arial', 14, 'bold')) my_btn.grid(row=6,column=0, columnspan= 2,padx=5,pady=5) #btn_clear = tk.Button(choice, text = "Clear track", command=lambda:slide("clear"),padx=10,pady=20,font = ('arial', 14, 'bold')) #btn_clear.grid(row=6,column = 3) ang1 = np.pi*A1/180 ang2 = np.pi*A2/180 x1 = r1*np.sin(ang1)+ xf y1 = r1*np.cos(ang1) + yf x2 = x1+r2*np.sin(ang2) y2 = y1+r2*np.cos(ang2) # # Create line # # create_line(x1,y1,x2,y2,fill="color") # #first pendulum line1 = my_canvas.create_line(xf,yf,x1,y1,fill = "black",width=4) circle1 = create_circle(x1,y1,m1,my_canvas) # # second pendulum line2 = my_canvas.create_line(x1,y1,x2,y2,fill = "black",width=4) circle2 = create_circle(x2,y2,m2,my_canvas) root.mainloop()