Orbital elements: Difference between revisions
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m (→{{header|Perl 6}}: link to the Clifford library) |
(Perl 5 translation) |
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TODO: pick an example from a reputable source. |
TODO: pick an example from a reputable source. |
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=={{header|Perl}}== |
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{{trans|Perl 6}} |
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<lang perl>use strict; |
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use warnings; |
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use Math::Vector::Real; |
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sub orbital_state_vectors { |
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my ( |
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$semimajor_axis, |
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$eccentricity, |
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$inclination, |
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$longitude_of_ascending_node, |
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$argument_of_periapsis, |
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$true_anomaly |
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) = @_[0..5]; |
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my ($i, $j, $k) = (V(1,0,0), V(0,1,0), V(0,0,1)); |
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sub rotate { |
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my $alpha = shift; |
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@_[0,1] = ( |
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+cos($alpha)*$_[0] + sin($alpha)*$_[1], |
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-sin($alpha)*$_[0] + cos($alpha)*$_[1] |
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); |
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} |
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rotate $longitude_of_ascending_node, $i, $j; |
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rotate $inclination, $j, $k; |
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rotate $argument_of_periapsis, $i, $j; |
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my $l = $eccentricity == 1 ? # PARABOLIC CASE |
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2*$semimajor_axis : |
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$semimajor_axis*(1 - $eccentricity**2); |
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my ($c, $s) = (cos($true_anomaly), sin($true_anomaly)); |
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my $r = $l/(1 + $eccentricity*$c); |
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my $rprime = $s*$r**2/$l; |
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my $position = $r*($c*$i + $s*$j); |
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my $speed = |
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($rprime*$c - $r*$s)*$i + ($rprime*$s + $r*$c)*$j; |
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$speed /= abs($speed); |
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$speed *= sqrt(2/$r - 1/$semimajor_axis); |
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{ |
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position => $position, |
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speed => $speed |
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} |
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} |
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use Data::Dumper; |
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print Dumper orbital_state_vectors |
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1, # semimajor axis |
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0.1, # eccentricity |
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0, # inclination |
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355/113/6, # longitude of ascending node |
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0, # argument of periapsis |
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0 # true-anomaly |
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; |
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</lang> |
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{{out}} |
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<pre>$VAR1 = { |
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'position' => bless( [ |
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'0.77942284339868', |
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'0.450000034653684', |
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'0' |
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], 'Math::Vector::Real' ), |
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'speed' => bless( [ |
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'-0.552770840960444', |
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'0.957427083179762', |
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'0' |
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], 'Math::Vector::Real' ) |
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};</pre> |
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=={{header|Perl 6}}== |
=={{header|Perl 6}}== |
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my \l = $eccentricity == 1 ?? # PARABOLIC CASE |
my \l = $eccentricity == 1 ?? # PARABOLIC CASE |
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2*$semimajor-axis !! |
2*$semimajor-axis !! |
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$semimajor-axis*(1 - $eccentricity**2); |
$semimajor-axis*(1 - $eccentricity**2); |
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my ($c, $s) = map {.($true-anomaly)}, &cos, &sin; |
my ($c, $s) = map {.($true-anomaly)}, &cos, &sin; |
Revision as of 13:59, 7 July 2016
Orbital elements is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
The purpose of this task is to convert orbital elements into orbital state vectors. It will be assumed that µ = GM = 1.
TODO: pick an example from a reputable source.
Perl
<lang perl>use strict; use warnings; use Math::Vector::Real;
sub orbital_state_vectors {
my ( $semimajor_axis, $eccentricity, $inclination, $longitude_of_ascending_node, $argument_of_periapsis, $true_anomaly ) = @_[0..5];
my ($i, $j, $k) = (V(1,0,0), V(0,1,0), V(0,0,1)); sub rotate { my $alpha = shift; @_[0,1] = ( +cos($alpha)*$_[0] + sin($alpha)*$_[1], -sin($alpha)*$_[0] + cos($alpha)*$_[1] ); }
rotate $longitude_of_ascending_node, $i, $j; rotate $inclination, $j, $k; rotate $argument_of_periapsis, $i, $j;
my $l = $eccentricity == 1 ? # PARABOLIC CASE 2*$semimajor_axis : $semimajor_axis*(1 - $eccentricity**2);
my ($c, $s) = (cos($true_anomaly), sin($true_anomaly));
my $r = $l/(1 + $eccentricity*$c); my $rprime = $s*$r**2/$l;
my $position = $r*($c*$i + $s*$j);
my $speed = ($rprime*$c - $r*$s)*$i + ($rprime*$s + $r*$c)*$j; $speed /= abs($speed); $speed *= sqrt(2/$r - 1/$semimajor_axis);
{ position => $position, speed => $speed }
}
use Data::Dumper;
print Dumper orbital_state_vectors
1, # semimajor axis 0.1, # eccentricity 0, # inclination 355/113/6, # longitude of ascending node 0, # argument of periapsis 0 # true-anomaly ;
</lang>
- Output:
$VAR1 = { 'position' => bless( [ '0.77942284339868', '0.450000034653684', '0' ], 'Math::Vector::Real' ), 'speed' => bless( [ '-0.552770840960444', '0.957427083179762', '0' ], 'Math::Vector::Real' ) };
Perl 6
We'll use the Clifford geometric algebra library but only for the vector operations.
<lang perl6>subset PositiveReal of Real where * >= 0; sub orbital-state-vectors(
PositiveReal :$semimajor-axis, PositiveReal :$eccentricity, Real :$inclination, Real :$longitude-of-ascending-node, Real :$argument-of-periapsis, Real :$true-anomaly
) {
use Clifford; my ($i, $j, $k) = @e[^3];
sub rotate($a is rw, $b is rw, Real \α) { ($a, $b) = cos(α)*$a + sin(α)*$b, -sin(α)*$a + cos(α)*$b; } rotate($i, $j, $longitude-of-ascending-node); rotate($j, $k, $inclination); rotate($i, $j, $argument-of-periapsis);
my \l = $eccentricity == 1 ?? # PARABOLIC CASE 2*$semimajor-axis !! $semimajor-axis*(1 - $eccentricity**2);
my ($c, $s) = map {.($true-anomaly)}, &cos, &sin;
my \r = l/(1 + $eccentricity*$c); my \rprime = $s*r**2/l;
my $position = r*($c*$i + $s*$j);
my $speed = (rprime*$c - r*$s)*$i + (rprime*$s + r*$c)*$j; $speed /= sqrt($speed**2); $speed *= sqrt(2/r - 1/$semimajor-axis);
{ :position($position X· @e[^3]), :speed($speed X· @e[^3]) }
}
say orbital-state-vectors
semimajor-axis => 1, eccentricity => 0.1, inclination => 0, longitude-of-ascending-node => pi/6, argument-of-periapsis => 0, true-anomaly => 0;
</lang>
- Output:
{position => (0.779422863405995 0.45 0), speed => (-0.552770798392567 0.957427107756338 0)}