1: #!/usr/bin/perl
   2: use strict;
   3: use warnings;
   4: 
   5: # Perl solving a physics / electrodynamics problem involving
   6: # symbolic mathematics, derivatives and complex numbers:
   7: 
   8: use Math::Symbolic qw/:all/;
   9: use Math::Complex;
  10: 
  11: # Given the following simple circuit:
  12: #
  13: #  ----|||||-----/\/\/\----       (R = resistor,
  14: # |      R          L      |       L = solenoid,
  15: # |                        |       U = alternating voltage)
  16: #  ---------O ~ O----------
  17: #            U(t)
  18: #
  19: # Question: What's the current in this circuit?
  20: #
  21: # We'll need some physics before letting the computer do the
  22: # math:
  23: # Applying Kirchhoff's rules, one quickly ends up with the
  24: # following differential equation for the current:
  25: #     (L * dI/dt) + (R * I)  =  U
  26: 
  27: my $left  = parse_from_string('L * total_derivative(I(t), t) + R * I(t)');
  28: my $right = parse_from_string('U(t)');
  29: 
  30: 
  31: # If we understand current and voltage to be complex functions,
  32: # we'll be able to derive. ("'" denoting complex here)
  33: #    I'(t) = I'_max * e^(i*omega*t)
  34: #    U'(t) = U_max  * e^(i*omega*t)
  35: # (Please note that omega is the frequency of the alternating voltage.
  36: # For example, the voltage from German outlets has a frequency of 50Hz.)
  37: 
  38: my $argument = parse_from_string('e^(i*omega*t)');
  39: my $current  = parse_from_string('I_max') * $argument;
  40: my $voltage  = parse_from_string('U_max') * $argument;
  41: 
  42: # Putting it into the equation:
  43: $left->implement( I  => $current );
  44: $right->implement( U => $voltage );
  45: 
  46: $left = $left->apply_derivatives()->simplify();
  47: 
  48: # Now, we can solve the equation to get a complex function for
  49: # the current:
  50: 
  51: $left  /= $argument;
  52: $right /= $argument;
  53: my $quotient = parse_from_string('R + i*omega*L');
  54: $left  /= $quotient;
  55: $right /= $quotient;
  56: 
  57: # Now we have:
  58: #    $left    = $right
  59: #    I_max(t) = U_max / (R + i*omega*L)
  60: # But I_max(t) is still complex and so is the right-hand-side of the
  61: # equation!
  62: 
  63: # Making the symbolic i a "literal" Math::Complex i
  64: $right->implement(
  65:     e => Math::Symbolic::Constant->euler(),
  66:     i => Math::Symbolic::Constant->new(i),    # Math::Complex magic
  67: );
  68: 
  69: print <<'HERE';
  70: Sample of complex maximum current with the following values:
  71:   U_max => 100
  72:   R     => 10
  73:   L     => 10
  74:   omega => 1
  75: HERE
  76: 
  77: print "Computed to: "
  78:   . $right->value(
  79:     U_max => 100,
  80:     R     => 10,
  81:     L     => 10,
  82:     omega => 1,
  83:   ),
  84:   "\n\n";
  85: 
  86: # Now, we're dealing with alternating current and voltage.
  87: # So let's make a generator that generates nice current
  88: # functions of time!
  89: #   I(t) = Re(I_max(t)) * cos(omega*t - phase);
  90: 
  91: # Usage: generate_current(U_Max, R, L, omega, phase)
  92: sub generate_current {
  93:     my $current = $right->new();    # cloning
  94: 
  95:     $current *= parse_from_string('cos(omega*t - phase)');
  96: 
  97:     $current->implement(
  98:         U_max => $_[0],
  99:         R     => $_[1],
 100:         L     => $_[2],
 101:         omega => $_[3],
 102:         phase => $_[4],
 103:     );
 104:     $current = $current->simplify();
 105:     return sub { Re( $current->value( t => $_[0] ) ) };
 106: }
 107: 
 108: print "Sample current function with: 230V, 2Ohms, 0.1H, 50Hz, PI/4\n";
 109: my $current_of_time = generate_current( 230, 2, 0.1, 50, PI / 4 );
 110: 
 111: print "The current at 0 seconds:   " . $current_of_time->(0) . "\n";
 112: print "The current at 0.1 seconds: " . $current_of_time->(0.1) . "\n";
 113: print "The current at 1 second:    " . $current_of_time->(1) . "\n";
 114: 
 115: </readmore>

Replies are listed 'Best First'.
Re: Solving electronics problems with Perl
by blue_cowdawg (Monsignor) on Feb 01, 2013 at 16:02 UTC

    and the question?

    Peter L. Berghold -- Unix Professional
    Peter -at- Berghold -dot- Net; AOL IM redcowdawg Yahoo IM: blue_cowdawg
[reply]
Re: Solving electronics problems with Perl
by Anonymous Monk on Feb 01, 2013 at 15:38 UTC 
    0: #!/usr/bin/perl
1: use strict;
2: use warnings;
3: 
4: # Perl solving a physics / electrodynamics problem involving
5: # symbolic mathematics, derivatives and complex numbers:
6: 
7: use Math::Symbolic qw/:all/;
8: use Math::Complex;
9: 
10: # Given the following simple circuit:
11: #
12: #  ----|||||-----/\/\/\----       (R = resistor,
13: # |      R          L      |       L = solenoid,
14: # |                        |       U = alternating voltage)
15: #  ---------O ~ O----------
16: #            U(t)
17: #
18: # Question: What's the current in this circuit?
19: #
20: # We'll need some physics before letting the computer do the
21: # math:
22: # Applying Kirchhoff's rules, one quickly ends up with the
23: # following differential equation for the current:
24: #     (L * dI/dt) + (R * I)  =  U
25: 
26: my $left  = parse_from_string('L * total_derivative(I(t), t) + R *
+ I(t)');
27: my $right = parse_from_string('U(t)');
28: 
29: <readmore>
30: # If we understand current and voltage to be complex functions,
31: # we'll be able to derive. ("'" denoting complex here)
32: #    I'(t) = I'_max * e^(i*omega*t)
33: #    U'(t) = U_max  * e^(i*omega*t)
34: # (Please note that omega is the frequency of the alternating volt
+age.
35: # For example, the voltage from German outlets has a frequency of 
+50Hz.)
36: 
37: my $argument = parse_from_string('e^(i*omega*t)');
38: my $current  = parse_from_string('I_max') * $argument;
39: my $voltage  = parse_from_string('U_max') * $argument;
40: 
41: # Putting it into the equation:
42: $left->implement( I  => $current );
43: $right->implement( U => $voltage );
44: 
45: $left = $left->apply_derivatives()->simplify();
46: 
47: # Now, we can solve the equation to get a complex function for
48: # the current:
49: 
50: $left  /= $argument;
51: $right /= $argument;
52: my $quotient = parse_from_string('R + i*omega*L');
53: $left  /= $quotient;
54: $right /= $quotient;
55: 
56: # Now we have:
57: #    $left    = $right
58: #    I_max(t) = U_max / (R + i*omega*L)
59: # But I_max(t) is still complex and so is the right-hand-side of t
+he
60: # equation!
61: 
62: # Making the symbolic i a "literal" Math::Complex i
63: $right->implement(
64:     e => Math::Symbolic::Constant->euler(),
65:     i => Math::Symbolic::Constant->new(i),    # Math::Complex magi
+c
66: );
67: 
68: print <<'HERE';
69: Sample of complex maximum current with the following values:
70:   U_max => 100
71:   R     => 10
72:   L     => 10
73:   omega => 1
74: HERE
75: 
76: print "Computed to: "
77:   . $right->value(
78:     U_max => 100,
79:     R     => 10,
80:     L     => 10,
81:     omega => 1,
82:   ),
83:   "\n\n";
84: 
85: # Now, we're dealing with alternating current and voltage.
86: # So let's make a generator that generates nice current
87: # functions of time!
88: #   I(t) = Re(I_max(t)) * cos(omega*t - phase);
89: 
90: # Usage: generate_current(U_Max, R, L, omega, phase)
91: sub generate_current {
92:     my $current = $right->new();    # cloning
93: 
94:     $current *= parse_from_string('cos(omega*t - phase)');
95: 
96:     $current->implement(
97:         U_max => $_[0],
98:         R     => $_[1],
99:         L     => $_[2],
100:         omega => $_[3],
101:         phase => $_[4],
102:     );
103:     $current = $current->simplify();
104:     return sub { Re( $current->value( t => $_[0] ) ) };
105: }
106: 
107: print "Sample current function with: 230V, 2Ohms, 0.1H, 50Hz, PI/
+4\n";
108: my $current_of_time = generate_current( 230, 2, 0.1, 50, PI / 4 )
+;
109: 
110: print "The current at 0 seconds:   " . $current_of_time->(0) . "\
+n";
111: print "The current at 0.1 seconds: " . $current_of_time->(0.1) . 
+"\n";
112: print "The current at 1 second:    " . $current_of_time->(1) . "\
+n";
113: 
114: </readmore>

    [download]
[reply]
[d/l]

      Dear Unknown Monk,
      Please use code tags. Is there a question in there somewhere? I can't tell...

      Peter L. Berghold -- Unix Professional
      Peter -at- Berghold -dot- Net; AOL IM redcowdawg Yahoo IM: blue_cowdawg
[reply]
Re: Solving electronics problems with Perl
by wolfger (Deacon) on Sep 08, 2003 at 15:53 UTC
    Really should have been a "read more" in there...

    Believe nothing, no matter where you read it, or who said it - even if I have said it - unless it agrees with your own reason and your own common sense. -- Buddha
[reply]
      I didn't dare to include a readmore tag because I don't trust the craft section's formatter. For example, it even screws up the greater-than characters on the front page that display correctly in the node itself.
[reply]

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