This code is based on the Tcl
pendulum.tcl demo. It presents a simple, rotational, pendulum; sets it in motion and draws the pendulum's phase space. The user can change the position of the pendulum by clicking in the
Pendulum Simulation panel.
# File: pendulum.py
# http://infohost.nmt.edu/tcc/help/pubs/tkinter//canvas.html
# Other Reference:
# http://rosettacode.org/wiki/Animate_a_pendulum#Python
import math
from tkinter import *
from tkinter import ttk
from demopanels import MsgPanel, SeeDismissPanel
class PendulumDemo(ttk.Frame):
def __init__(self, isapp=True, name='pendulumdemo'):
ttk.Frame.__init__(self, name=name)
self.pack(expand=Y, fill=BOTH)
self.master.title('Pendulum Demo')
self.isapp = isapp
self._create_widgets()
def _create_widgets(self):
if self.isapp:
MsgPanel(self,
["This demonstration shows how Tkinter can be used to carry out animations ",
"that are linked to simulations of physical systems. In the left canvas ",
"is a graphical representation of the physical system itself, a simple ",
"pendulum, and in the right canvas is a graph of the phase space of the ",
"system, which is a plot of the angle (relative to the vertical) against ",
"the angular velocity. The pendulum bob may be repositioned by clicking ",
"and dragging anywhere on the left canvas."])
SeeDismissPanel(self)
self._create_demo_panel()
def _create_demo_panel(self):
demoPanel = ttk.Frame(self, name='demo')
demoPanel.pack(side=TOP, fill=BOTH, expand=Y)
# variables used by the widgets
self.__theta = 45.0 # pendulum angle
self.__dtheta = 0.0 # new pendulum angle
self.__length = 150 # rod length
self.__home = 160 # rod 'attach' position
self.__points = [] # coords describing phase motion
self.__psw = 320/2 # phase space panel width
self.__psh = 200/2 # phase space panel height
# tag and colour names for the phase space oval which
# is drawn in segments to allow colour variations
# (in a dict to avoid building/discarding strings during animation)
self.__graph = {0: ('graph0','grey0'), 10: ('graph10','grey10'),
20: ('graph20', 'grey20'), 30: ('graph30','grey30'),
40: ('graph40','grey40'), 50: ('graph50','grey50'),
60: ('graph60','grey60'), 70: ('graph70','grey70'),
80: ('graph80','grey80'), 90: ('graph90','grey90')}
# build panels
pw = ttk.Panedwindow(demoPanel, orient=HORIZONTAL)
pw.pack(side=TOP, fill=BOTH, expand=Y)
self.__pen = self._create_pendulum_panel(pw)
self.__phase = self._create_phase_panel(pw)
self._show_pendulum()
# add bindings
self._create_bindings()
# start animations after slight pause
self.after(500, self._repeat)
# =====================================================================================
# Animation handler
# =====================================================================================
def _repeat(self):
self._recompute_angle() # define pendulum position and swing parameters
self._show_pendulum() # display pendulum
self._show_phase() # display phase space
self.after(15, self._repeat) # repeat animation
# =====================================================================================
# Bindings and bound methods
# =====================================================================================
def _create_bindings(self):
# allow user to re-position pendulum with Left Mouse button click
self.__pen.bind('<1>', self._change_pendulum)
self.__pen.bind('<B1-Motion>', self._change_pendulum)
self.__pen.bind('<ButtonRelease-1>', lambda e, repeat=True: self._change_pendulum(e, repeat))
# capture window resize and resize phase space panel
self.__phase.bind('<Configure>', self._phase_configure)
def _change_pendulum(self, evt, repeat=False):
# triggered when user clicks in 'Pendulum Simulation' panel
# re-positions the pendulum bob and resizes the rod
self._show_pendulum(evt.x, evt.y)
if repeat:
self.after(15, self._repeat)
def _phase_configure(self, evt):
# triggered when the user resizes the window
# resizes the phase space panel
width = self.__phase.winfo_width()
height = self.__phase.winfo_height()
self.__psh = height / 2
self.__psw = width / 2
self.__phase.coords('x_axis', 2, self.__psh, width-2, self.__psh )
self.__phase.coords('y_axis', self.__psw, height-2, self.__psw, 2)
self.__phase.coords('label_dtheta', self.__psw-4, 6)
self.__phase.coords('label_theta', width-6, self.__psh+4)
# =====================================================================================
# Routines to build and control the pendulum
# =====================================================================================
def _create_pendulum_panel(self, parent):
left = ttk.Labelframe(parent, text="Pendulum Simulation")
parent.add(left)
# Create the canvas containing the graphical representation of the
# simulated system
c = Canvas(left, width=320, height=200, background='white',
bd=2, relief=SUNKEN, name='pen_canvas')
c.create_text(5, 5, anchor='nw', text='Click to Adjust Bob Start Position',
state='disabled', disabledfill='grey50')
c.create_line(0,25,320,25, tags='plate', fill='grey50', width=2)
c.create_oval(155,20,165,30, tags='pivot', fill='grey50')
c.create_line(1,1,1,1, tags='rod', fill='black', width=3)
c.create_oval(1,1,2,2, tags='bob', fill='yellow', outline='black')
c.pack(fill=BOTH, expand=Y)
return c
def _show_pendulum(self, x=None, y=None):
# display the pendulum
if (x and y) and (x != self.__home or y != 25):
self.__dtheta = 0.0
x2 = x - self.__home
y2 = y - 25
self.__length = math.hypot(x2,y2)
self.__theta = math.atan2(x2, y2) * 180/math.pi
else:
angle = math.radians(self.__theta)
x = self.__home + self.__length * math.sin(angle)
y = 25 + self.__length * math.cos(angle)
self.__pen.coords('rod', self.__home, 25, x, y)
self.__pen.coords('bob', x-15, y-15, x+15, y+15)
def _recompute_angle(self):
# core animation routine for a simple rotational
# pendulum; recomputes the angle parameters
# (the original Tcl file says there is a better
# way to do this but it requires a better knowledge
# of derivatives)
scaling = 3000.0/self.__length/self.__length
# first estimate
firstDDtheta = -math.sin(math.radians(self.__theta)) * scaling
midDtheta = self.__dtheta + firstDDtheta
midtheta = self.__theta + (self.__dtheta + midDtheta)/2.0
# second estimate
midDDtheta = -math.sin(math.radians(midtheta)) * scaling
midDtheta = self.__dtheta + (firstDDtheta + midDDtheta)/2.0
midtheta = self.__theta + (self.__dtheta + midDtheta)/2.0
# first double estimate
midDDtheta = -math.sin(math.radians(midtheta)) * scaling
lastDtheta = midDtheta + midDDtheta
lasttheta = midtheta + (midDtheta + lastDtheta)/2.0
# second double estimate
lastDDtheta = -math.sin(math.radians(lasttheta)) * scaling
lastDtheta = midDtheta + (midDDtheta + lastDDtheta)/2.0
lasttheta = midtheta + (midDtheta + lastDtheta)/2.0
self.__theta = lasttheta
self.__dtheta = lastDtheta
# =====================================================================================
# Routines to build and control the phase space
# =====================================================================================
def _create_phase_panel(self, parent):
right = ttk.Labelframe(parent, text="Phase Space")
parent.add(right)
# Create the canvas containing the phase space graph; this consists of
# a line that gets gradually paler as it ages, which is an effective
# visual trick.
c = Canvas(right, width=320, height=200, background='white',
bd=2, relief=SUNKEN, name='phase_canvas')
c.create_line(160,200,160,0, fill='grey75', arrow='last', tags='y_axis')
c.create_line(0,100,320,100, fill='grey75', arrow='last', tags='x_axis')
for i in range(90, -1, -10):
c.create_line(0,0,1,1, smooth='true', tags=self.__graph[i][0],
fill=self.__graph[i][1])
c.create_text(0,0, anchor='ne', text='q', font=('Symbol', 8),
tags='label_theta')
c.create_text(0,0, anchor='ne', text='dq', font=('Symbol', 8),
tags='label_dtheta')
c.pack(fill=BOTH, expand=Y)
return c
def _show_phase(self):
# Update the phase-space graph according to the current angle and the
# rate at which the angle is changing (the first derivative with
# respect to time.)
self.__points.extend([self.__theta+self.__psw,
-20 * self.__dtheta+self.__psh])
end = len(self.__points)
if end > 100: # start over
self.__points = []
pts = []
for i in range(0,100,10):
pts = self.__points[end-i:end-i-12]
if len(pts) >= 4: # coords for affected portion of the line
self.__phase.coords(self.__graph[i][0], *pts)
if __name__ == '__main__':
PendulumDemo().mainloop()
