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| import pylab | |
| from Tkinter import * | |
| from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg, NavigationToolbar2TkAgg | |
| from matplotlib.figure import Figure | |
| from mpl_toolkits.mplot3d import Axes3D | |
| from matplotlib import cm | |
| import numpy as np | |
| class ParticleMotion: | |
| def __init__(self, master): | |
| frame = Frame(master) | |
| frame.grid(column = 0, row = 0) | |
| frame.grid() | |
| self.makeInputs(frame) | |
| self.makeOutputs(frame) | |
| self.makePlot(frame) | |
| self.Ex = (self.eex.get()) | |
| self.Ey = (self.eey.get()) | |
| self.Ez = (self.eez.get()) | |
| self.Bx = (self.ebx.get()) | |
| self.By = (self.eby.get()) | |
| self.Bz = (self.ebz.get()) | |
| self.m = (self.em.get()) # Mass of the particle | |
| self.q = (self.eq.get()) # Charge | |
| self.x1 = (self.ex1.get()) # initial position x | |
| self.y1 = (self.ey1.get()) # initial position y | |
| self.z1 = (self.ez1.get()) # initial position z | |
| self.vx = (self.evx.get()) # initial velocity vx | |
| self.vy = (self.evy.get()) # initial velocity vy | |
| self.vz = (self.evz.get()) # initial velocity vz | |
| self.dt = (self.edt.get()) | |
| self.t = (self.et.get()) | |
| def makePlot(self, frame): | |
| self.fig = Figure(figsize=(10,8), dpi=100) | |
| self.canvas = FigureCanvasTkAgg(self.fig, frame) | |
| self.canvas.show() | |
| self.canvas.get_tk_widget().grid(column = 1, row = 0) | |
| self.toolbar = NavigationToolbar2TkAgg(self.canvas, frame) | |
| self.toolbar.update() | |
| self.toolbar.grid(column = 1, row = 7) | |
| def makeInputs(self, frame): | |
| InputFrame = Frame(frame) | |
| InputFrame.grid(column = 0, row = 0) | |
| self.lbln = Label(InputFrame, text = "Set a value for Ex", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 0) | |
| self.eex = Entry(InputFrame) | |
| self.eex.insert(0, "0.0") | |
| self.eex.grid(column = 1, row = 0) | |
| self.lbln = Label(InputFrame, text = "Set a value for Ey", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 1) | |
| self.eey = Entry(InputFrame) | |
| self.eey.insert(0, "2.0") | |
| self.eey.grid(column = 1, row = 1) | |
| self.lbln = Label(InputFrame, text = "Set a value for Ez", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 2) | |
| self.eez = Entry(InputFrame) | |
| self.eez.insert(0, "0.0") | |
| self.eez.grid(column = 1, row = 2) | |
| self.lbln = Label(InputFrame, text = "Set a value for Bx", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 3) | |
| self.ebx = Entry(InputFrame) | |
| self.ebx.insert(0, "0.0") | |
| self.ebx.grid(column = 1, row = 3) | |
| self.lbln = Label(InputFrame, text = "Set a value for By", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 4) | |
| self.eby = Entry(InputFrame) | |
| self.eby.insert(0, "0.0") | |
| self.eby.grid(column = 1, row = 4) | |
| self.lbln = Label(InputFrame, text = "Set a value for Bz", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 5) | |
| self.ebz = Entry(InputFrame) | |
| self.ebz.insert(0, "4.0") | |
| self.ebz.grid(column = 1, row = 5) | |
| self.lbln = Label(InputFrame, text = "Set a value for m", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 6) | |
| self.em = Entry(InputFrame) | |
| self.em.insert(0, "2.0") | |
| self.em.grid(column = 1, row = 6) | |
| self.lbln = Label(InputFrame, text = "Set a value for q", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 7) | |
| self.eq = Entry(InputFrame) | |
| self.eq.insert(0, "5.0") | |
| self.eq.grid(column = 1, row = 7) | |
| self.lbln = Label(InputFrame, text = "Set a value for x0", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 8) | |
| self.ex1 = Entry(InputFrame) | |
| self.ex1.insert(0, "0.0") | |
| self.ex1.grid(column = 1, row = 8) | |
| self.lbln = Label(InputFrame, text = "Set a value for y0", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 9) | |
| self.ey1 = Entry(InputFrame) | |
| self.ey1.insert(0, "0.0") | |
| self.ey1.grid(column = 1, row = 9) | |
| self.lbln = Label(InputFrame, text = "Set a value for z0", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 10) | |
| self.ez1 = Entry(InputFrame) | |
| self.ez1.insert(0, "0.0") | |
| self.ez1.grid(column = 1, row = 10) | |
| self.lbln = Label(InputFrame, text = "Set a value for vx", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 11) | |
| self.evx = Entry(InputFrame) | |
| self.evx.insert(0, "20.0") | |
| self.evx.grid(column = 1, row = 11) | |
| self.lbln = Label(InputFrame, text = "Set a value for vy", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 12) | |
| self.evy = Entry(InputFrame) | |
| self.evy.insert(0, "10.0") | |
| self.evy.grid(column = 1, row = 12) | |
| self.lbln = Label(InputFrame, text = "Set a value for vz", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 13) | |
| self.evz = Entry(InputFrame) | |
| self.evz.insert(0, "2.0") | |
| self.evz.grid(column = 1, row = 13) | |
| self.lbln = Label(InputFrame, text = "Set a value for dt", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 14) | |
| self.edt = Entry(InputFrame) | |
| self.edt.insert(0, "0.001") | |
| self.edt.grid(column = 1, row = 14) | |
| self.lbln = Label(InputFrame, text = "Set a value for t0", justify=LEFT) | |
| self.lbln.grid(column = 0, row = 15) | |
| self.et = Entry(InputFrame) | |
| self.et.insert(0, "0.0") | |
| self.et.grid(column = 1, row = 15) | |
| def euler(self): | |
| self.Ex = (self.eex.get()) | |
| self.Ey = (self.eey.get()) | |
| self.Ez = (self.eez.get()) | |
| self.Bx = (self.ebx.get()) | |
| self.By = (self.eby.get()) | |
| self.Bz = (self.ebz.get()) | |
| self.m = (self.em.get()) # Mass of the particle | |
| self.q = (self.eq.get()) # Charge | |
| self.x1 = (self.ex1.get()) # initial position x | |
| self.y1 = (self.ey1.get()) # initial position y | |
| self.z1 = (self.ez1.get()) # initial position z | |
| self.vx = (self.evx.get()) # initial velocity vx | |
| self.vy = (self.evy.get()) # initial velocity vy | |
| self.vz = (self.evz.get()) # initial velocity vz | |
| self.dt = (self.edt.get()) | |
| self.t = (self.et.get()) | |
| self.d = [] | |
| self.e = [] | |
| self.f = [] | |
| while self.t < 10: # trace path until time reaches value e.g. 10 | |
| self.Fx = self.q * (self.Ex + (self.vy * self.Bz) - (self.vz * self.By) ) | |
| self.Fy = self.q * (self.Ey - (self.vx * self.Bz) + (self.vz * self.Bx) ) | |
| self.Fz = self.q * (self.Ez + (self.vx * self.By) - (self.vy * self.Bx) ) | |
| self.vx = self.vx + self.Fx/self.m * self.dt # Acceleration = F/m; dv = a.dt | |
| self.vy = self.vy + self.Fy/self.m * self.dt | |
| self.vz = self.vz + self.Fz/self.m * self.dt | |
| self.x = self.x + self.vx * self.dt | |
| self.y = self.y + self.vy * self.dt | |
| self.z = self.z + self.vz * self.dt | |
| self.d.append(x) | |
| self.e.append(y) | |
| self.f.append(z) | |
| self.t += self.dt | |
| ax = Axes3D(self.fig) | |
| ax.plot3D(self.d,self.e,self.f, color='green', label='path') | |
| ax.set_title("Path of charged particle under influence of electric and magnetic fields(Euler)") | |
| ax.set_xlabel('X') | |
| ax.set_ylabel('Y') | |
| ax.set_zlabel('Z') | |
| self.canvas.show() | |
| def RK4(self): | |
| self.Ex = (self.eex.get()) | |
| self.Ey = (self.eey.get()) | |
| self.Ez = (self.eez.get()) | |
| self.Bx = (self.ebx.get()) | |
| self.By = (self.eby.get()) | |
| self.Bz = (self.ebz.get()) | |
| self.m = (self.em.get()) # Mass of the particle | |
| self.q = (self.eq.get()) # Charge | |
| self.x1 = (self.ex1.get()) # initial position x | |
| self.y1 = (self.ey1.get()) # initial position y | |
| self.z1 = (self.ez1.get()) # initial position z | |
| self.vx = (self.evx.get()) # initial velocity vx | |
| self.vy = (self.evy.get()) # initial velocity vy | |
| self.vz = (self.evz.get()) # initial velocity vz | |
| self.dt = (self.edt.get()) | |
| self.t = (self.et.get()) | |
| self.a = [] | |
| self.b = [] | |
| self.c = [] | |
| while self.t < 10: # trace path until time reaches value e.g. 10 | |
| k1x = velocx(self.vy, self.vz) | |
| k2x = velocx(self.vy + (1/2.0)*k1x, self.vz + (1/2.0)*k1x) | |
| k3x = velocx(self.vy + (1/2.0)*k2x, self.vz + (1/2.0)*k1x) | |
| k4x = velocx(self.vy + k3x, self.vz + k3x) | |
| self.vx += (1.0/6.0)*(k1x + 2*k2x + 2*k3x + k4x) | |
| self.x1 += self.vx *self.dt | |
| k1y = velocy(self.vx, self.vz) | |
| k2y = velocy(self.vx + (1/2.0)*k1y, self.vz + (1/2.0)*k1y) | |
| k3y = velocy(self.vx + (1/2.0)*k2y, self.vz + (1/2.0)*k1y) | |
| k4y = velocy(self.vx + k3y, self.vz + k3y) | |
| self.vy += (1.0/6.0)*(k1y + 2*k2y + 2*k3y + k4y) | |
| self.y1 += self.vy*self.dt | |
| k1z = velocz(self.vx, self.vy) | |
| k2z = velocz(self.vx + (1/2.0)*k1z, self.vy + (1/2.0)*k1z) | |
| k3z = velocz(self.vx + (1/2.0)*k2z, self.vy + (1/2.0)*k1z) | |
| k4z = velocz(self.vx + k3z, self.vy + k3z) | |
| self.vz += (1.0/6.0)*(k1z + 2*k2z + 2*k3z + k4z) | |
| self.z1 += self.vz*self.dt | |
| self.a.append(self.x1) | |
| self.b.append(self.y1) | |
| self.c.append(self.z1) | |
| self.t += self.dt | |
| ax = Axes3D(self.fig) | |
| ax.plot3D(self.a,self.b,self.c, color='green', label='path') | |
| ax.set_title("Path of charged particle under influence of electric and magnetic fields(RK4)") | |
| ax.set_xlabel('X') | |
| ax.set_ylabel('Y') | |
| ax.set_zlabel('Z') | |
| self.canvas.show() | |
| print(self.Ex, | |
| self.Ey, | |
| self.Ez, | |
| self.Bx, | |
| self.By, | |
| self.Bz, | |
| self.m, | |
| self.q, | |
| self.x1, | |
| self.y1, | |
| self.z1, | |
| self.vx, | |
| self.vy, | |
| self.vz, | |
| self.dt, | |
| self.t, | |
| self.a, | |
| self.b, | |
| self.c) | |
| def makeOutputs(self, frame): | |
| OutputFrame = Frame(frame) | |
| OutputFrame.grid(column = 0, row = 16) | |
| self.bt = Button(OutputFrame, text="GO RK4", width=10, command=self.RK4) | |
| self.bt.grid(column = 1, row = 0) | |
| self.bE= Button(OutputFrame, text="GO EULER", width=10, command=self.euler) | |
| self.bE.grid(column = 1, row = 1) | |
| root = Tk() | |
| test = ParticleMotion(root) | |
| root.mainloop() |
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