summaryrefslogtreecommitdiffstats
path: root/library/demos/pendulum.tcl
blob: cb31b330394aad1df33d11bee2fbe0b6e9a94ad9 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
# pendulum.tcl --
#
# This demonstration illustrates how Tcl/Tk can be used to construct
# simulations of physical systems.
#
# RCS: @(#) $Id: pendulum.tcl,v 1.2 2004/12/21 11:56:35 dkf Exp $

if {![info exists widgetDemo]} {
    error "This script should be run from the \"widget\" demo."
}

package require Tk

set w .pendulum
catch {destroy $w}
toplevel $w
wm title . "Pendulum Animation Demonstration"
wm iconname $w "pendulum"
positionWindow $w

label $w.msg -font $font -wraplength 4i -justify left -text "This demonstration shows how Tcl/Tk 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."
pack $w.msg

## See Code / Dismiss buttons
set btns [addSeeDismiss $w.buttons $w]
pack $btns -side bottom -fill x

# Create some structural widgets
pack [panedwindow $w.p] -fill both -expand 1
$w.p add [labelframe $w.p.l1 -text "Pendulum Simulation"]
$w.p add [labelframe $w.p.l2 -text "Phase Space"]

# Create the canvas containing the graphical representation of the
# simulated system.
canvas $w.c -width 320 -height 200 -background white -bd 2 -relief sunken
$w.c create text 5 5 -anchor nw -text "Click to Adjust Bob Start Position"
# Coordinates of these items don't matter; they will be set properly below
$w.c create line 0 25 320 25 -width 2 -fill grey50 -tags plate
$w.c create line 1 1 1 1 -tags pendulumRod -width 3 -fill black
$w.c create oval 1 1 2 2 -tags pendulumBob -fill yellow -outline black
$w.c create oval 155 20 165 30 -fill grey50 -outline {}
pack $w.c -in $w.p.l1 -fill both -expand true

# Create the canvas containing the phase space graph; this consists of
# a line that gets gradually paler as it ages, which is an extremely
# effective visual trick.
canvas $w.k -width 320 -height 200 -background white -bd 2 -relief sunken
$w.k create line 160 200 160 0 -fill grey75 -arrow last -tags y_axis
$w.k create line 0 100 320 100 -fill grey75 -arrow last -tags x_axis
for {set i 90} {$i>=0} {incr i -10} {
    # Coordinates of these items don't matter; they will be set properly below
    $w.k create line 0 0 1 1 -smooth true -tags graph$i -fill grey$i
}
# FIXME: UNICODE labels
$w.k create text 0 0 -anchor ne -text "q" -font {Symbol 8} -tags label_theta
$w.k create text 0 0 -anchor ne -text "dq" -font {Symbol 8} -tags label_dtheta
pack $w.k -in $w.p.l2 -fill both -expand true

# Initialize some variables
set points {}
set Theta   45.0
set dTheta   0.0
set pi       3.1415926535897933
set length 150

# This procedure makes the pendulum appear at the correct place on the
# canvas. If the additional arguments "at $x $y" are passed (the 'at'
# is really just syntactic sugar) instead of computing the position of
# the pendulum from the length of the pendulum rod and its angle, the
# length and angle are computed in reverse from the given location
# (which is taken to be the centre of the pendulum bob.)
proc showPendulum {canvas {at {}} {x {}} {y {}}} {
    global Theta dTheta pi length
    if {$at eq "at" && ($x!=160 || $y!=25)} {
	set dTheta 0.0
	set x2 [expr {$x-160}]
	set y2 [expr {$y-25}]
	set length [expr {hypot($x2,$y2)}]
	set Theta [expr {atan2($x2,$y2)*180/$pi}]
    } else {
	set angle [expr {$Theta * $pi/180}]
	set x [expr {160+$length*sin($angle)}]
	set y [expr {25+$length*cos($angle)}]
    }
    $canvas coords pendulumRod 160 25 $x $y
    $canvas coords pendulumBob \
	    [expr {$x-15}] [expr {$y-15}] [expr {$x+15}] [expr {$y+15}]
}
showPendulum $w.c

# 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.)
proc showPhase {canvas} {
    global Theta dTheta points psw psh
    lappend points [expr {$Theta+$psw}] [expr {-20*$dTheta+$psh}]
    if {[llength $points] > 100} {
    	 set points [lrange $points end-99 end]
    }
    for {set i 0} {$i<100} {incr i 10} {
	set list [lrange $points end-[expr {$i-1}] end-[expr {$i-12}]]
	if {[llength $list] >= 4} {
	    $canvas coords graph$i $list
	}
    }
}

# Set up some bindings on the canvases.  Note that when the user
# clicks we stop the animation until they release the mouse
# button. Also note that both canvases are sensitive to <Configure>
# events, which allows them to find out when they have been resized by
# the user.
bind $w.c <Destroy> {
    after cancel $animationCallbacks(pendulum)
    unset animationCallbacks(pendulum)
}
bind $w.c <1> {
    after cancel $animationCallbacks(pendulum)
    showPendulum %W at %x %y
}
bind $w.c <B1-Motion> {
    showPendulum %W at %x %y
}
bind $w.c <ButtonRelease-1> {
    showPendulum %W at %x %y
    set animationCallbacks(pendulum) [after 15 repeat [winfo toplevel %W]]
}
bind $w.c <Configure> {
    %W coords plate 0 25 %w 25
}
bind $w.k <Configure> {
    set psh [expr %h/2]
    set psw [expr %w/2]
    %W coords x_axis 2 $psh [expr %w-2] $psh
    %W coords y_axis $psw [expr %h-2] $psw 2
    %W coords label_dtheta [expr $psw-4] 6
    %W coords label_theta [expr %w-6] [expr $psh+4]
}

# This procedure is the "business" part of the simulation that does
# simple numerical integration of the formula for a simple rotational
# pendulum.
proc recomputeAngle {} {
    global Theta dTheta pi length
    set scaling [expr {3000.0/$length/$length}]

    # To estimate the integration accurately, we really need to
    # compute the end-point of our time-step.  But to do *that*, we
    # need to estimate the integration accurately!  So we try this
    # technique, which is inaccurate, but better than doing it in a
    # single step.  What we really want is bound up in the
    # differential equation:
    #       ..             - sin theta
    #      theta + theta = -----------
    #                         length
    # But my math skills are not good enough to solve this!

    # first estimate
    set firstDDTheta [expr {-sin($Theta * $pi/180)*$scaling}]
    set midDTheta [expr {$dTheta + $firstDDTheta}]
    set midTheta [expr {$Theta + ($dTheta + $midDTheta)/2}]
    # second estimate
    set midDDTheta [expr {-sin($midTheta * $pi/180)*$scaling}]
    set midDTheta [expr {$dTheta + ($firstDDTheta + $midDDTheta)/2}]
    set midTheta [expr {$Theta + ($dTheta + $midDTheta)/2}]
    # Now we do a double-estimate approach for getting the final value
    # first estimate
    set midDDTheta [expr {-sin($midTheta * $pi/180)*$scaling}]
    set lastDTheta [expr {$midDTheta + $midDDTheta}]
    set lastTheta [expr {$midTheta + ($midDTheta + $lastDTheta)/2}]
    # second estimate
    set lastDDTheta [expr {-sin($lastTheta * $pi/180)*$scaling}]
    set lastDTheta [expr {$midDTheta + ($midDDTheta + $lastDDTheta)/2}]
    set lastTheta [expr {$midTheta + ($midDTheta + $lastDTheta)/2}]
    # Now put the values back in our globals
    set dTheta $lastDTheta
    set Theta $lastTheta
}

# This method ties together the simulation engine and the graphical
# display code that visualizes it.
proc repeat w {
    global animationCallbacks

    # Simulate
    recomputeAngle

    # Update the display
    showPendulum $w.c
    showPhase $w.k

    # Reschedule ourselves
    set animationCallbacks(pendulum) [after 15 [list repeat $w]]
}
# Start the simulation after a short pause
set animationCallbacks(pendulum) [after 500 [list repeat $w]]