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Orbital elements: Difference between revisions
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<pre>Position : (0.7794228433986797, 0.45000003465368416, 0.0)
Speed : (-0.5527708409604438, 0.9574270831797618, 0.0)</pre>
=={{header|Nim}}==
{{trans|Kotlin}}
<lang Nim>import math, strformat
type Vector = tuple[x, y, z: float]
func `+`(v1, v2: Vector): Vector = (v1.x + v2.x, v1.y + v2.y, v1.z + v2.z)
func `*`(v: Vector; m: float): Vector = (v.x * m, v.y * m, v.z * m)
func `*=`(v: var Vector; m: float) = v.x *= m; v.y *= m; v.z *= m
func `/=`(v: var Vector; d: float) = v.x /= d; v.y /= d; v.z /= d
func abs(v: Vector): float = sqrt(v.x * v.x + v.y * v.y + v.z * v.z)
func `$`(v: Vector): string = &"({v.x}, {v.y}, {v.z})"
func orbitalStateVectors(semimajorAxis: float,
eccentricity: float,
inclination: float,
longitudeOfAscendingNode: float,
argumentOfPeriapsis: float,
trueAnomaly: float): tuple[position, speed: Vector] =
var
i: Vector = (1.0, 0.0, 0.0)
j: Vector = (0.0, 1.0, 0.0)
k: Vector = (0.0, 0.0, 1.0)
func mulAdd(v1: Vector; x1: float; v2: Vector; x2: float): Vector = v1 * x1 + v2 * x2
func rotate(a, b: Vector; alpha: float): (Vector, Vector) =
(mulAdd(a, cos(alpha), b, sin(alpha)), mulAdd(a, -sin(alpha), b, cos(alpha)))
var p = rotate(i, j, longitudeOfAscendingNode)
(i, j) = p
p = rotate(j, k, inclination)
j = p[0]
p = rotate(i, j, argumentOfPeriapsis)
(i, j) = p
let
l = semimajorAxis * (if eccentricity == 1: 2.0 else: 1.0 - eccentricity * eccentricity)
c = cos(trueAnomaly)
s = sin(trueAnomaly)
r = l / (1.0 + eccentricity * c)
rprime = s * r * r / l
result.position = mulAdd(i, c, j, s) * r
result.speed = mulAdd(i, rprime * c - r * s, j, rprime * s + r * c)
result.speed /= abs(result.speed)
result.speed *= sqrt(2 / r - 1 / semimajorAxis)
let (position, speed) = orbitalStateVectors(semimajorAxis = 1.0,
eccentricity = 0.1,
inclination = 0.0,
longitudeOfAscendingNode = 355.0 / (113.0 * 6.0),
argumentOfPeriapsis = 0.0,
trueAnomaly = 0.0)
echo "Position: ", position
echo "Speed: ", speed</lang>
{{out}}
<pre>Position: (0.7794228433986797, 0.4500000346536842, 0.0)
Speed: (-0.5527708409604438, 0.9574270831797618, 0.0)</pre>
=={{header|ooRexx}}==
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