From 46afb6bf501f4001c4bdb7bd2f2db7c466f95554 Mon Sep 17 00:00:00 2001
From: Juan Marin Noguera <juan@mnpi.eu>
Date: Tue, 25 Jul 2023 18:22:04 +0200
Subject: Solvned project from 2020

Note that Go didn't have generics back then.
---
 ivp/arenstorf.go | 68 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 68 insertions(+)
 create mode 100644 ivp/arenstorf.go

(limited to 'ivp/arenstorf.go')

diff --git a/ivp/arenstorf.go b/ivp/arenstorf.go
new file mode 100644
index 0000000..05b1527
--- /dev/null
+++ b/ivp/arenstorf.go
@@ -0,0 +1,68 @@
+// Arenstorf orbit problem.
+//
+// Copyright (C) 2020 Juan Marín Noguera
+//
+// This file is part of Solvned.
+//
+// Solvned is free software: you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License as published by the Free
+// Software Foundation, either version 3 of the License, or (at your option) any 
+// later version.
+//
+// Solvned is distributed in the hope that it will be useful, but WITHOUT ANY 
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
+// A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
+// details.
+//
+// You should have received a copy of the GNU Lesser General Public License
+// along with Solvned. If not, see <https://www.gnu.org/licenses/>.
+
+package ivp
+
+import (
+	"math"
+	"github.com/JwanMan/mned"
+)
+
+var arenstorfOrbit = mned.IVP{
+	Derivative: func(p mned.Point) ([]float64, bool) {
+		const μ = 0.012277471
+		const μ2 = 1 - μ
+		xμ := p.Value[0] + μ
+		xμ2 := p.Value[0] - μ2
+		D1 := xμ*xμ + p.Value[1]*p.Value[1]
+		D1 *= math.Sqrt(D1)
+		D2 := xμ2*xμ2 + p.Value[1]*p.Value[1]
+		D2 *= math.Sqrt(D2)
+		return []float64{
+			p.Value[2],
+			p.Value[3],
+			p.Value[0] + 2*p.Value[3] - μ2*xμ/D1 - μ*xμ2/D2,
+			p.Value[1]*(1-μ2/D1-μ/D2) - 2*p.Value[2],
+		}, true
+	},
+	Start: mned.Point{
+		Time:  0,
+		Value: []float64{0.994, 0, 0, -2.001585106},
+	},
+}
+
+// The Arenstorf orbit is a stable orbit of a satellite around the Earth taking
+// into account the gravity of the Earth and the Moon and considering the
+// satellite to have a negligible mass compared to both. The orbit was
+// discovered by Richard Arenstorf and is given by the following formulae:
+//
+// ```
+// μ = 0.012277471, μ' = 1 - μ;
+// D1 = ((x+μ)^2 + y^2)^(3/2), D2 = ((x-μ')^2 + y^2)^(3/2);
+// x" = x + 2y' - μ'(x+μ)/D1 - μ(x-μ')/D2;
+// y" = y - 2x' - μ'y/D1 - μy/D2;
+// x(0) = 0.994, y(0) = 0, x'(0) = 0, y'(0) = -2.001585106.
+// ```
+//
+// The orbit has three big loops at one side and a small one at the other, and
+// varying μ changes the number of loops. Because of the unstability, this
+// problem is often used to test different ODE solving methods.
+func ArenstorfOrbit() mned.IVP {
+	return arenstorfOrbit.Clone()
+}
-- 
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