From 5dd72d28b99d7fff6649c4f7d1f45d2adee49759 Mon Sep 17 00:00:00 2001
From: Anson <anson@ansonbiggs.com>
Date: Sat, 14 Aug 2021 23:28:20 -0700
Subject: [PATCH] tried swapping quaternions example with orbits

---
 index.jl | 110 ++++++++++++++++++++++++++-----------------------------
 1 file changed, 51 insertions(+), 59 deletions(-)

diff --git a/index.jl b/index.jl
index 8fdb45c..b0c8693 100644
--- a/index.jl
+++ b/index.jl
@@ -375,71 +375,61 @@ md"""
 ### Custom Data Types
 """
 
+# ╔═╡ f6d87354-ac46-4202-92f8-b39a0db13327
+μ = 3.986004418e14u"m^3/s^2" # Standard Gravitational Parameter for Earth
+
 # ╔═╡ 44daff45-f608-47e3-ad6e-fca43532f322
-struct Quaternion
-	i::Float64
-	j::Float64
-	k::Float64
-	r::Float64
+struct Elliptic_Orbit
+	"""Simple 2d elliptic orbit"""
+	r::typeof(.1u"km") # altitude
+	a::typeof(.1u"km") # semimajor axis
+	e::Float64 # eccentricity
 	
-	Quaternion(i, j, k, r) = norm([i, j, k, r]) ≈ 1 ? new(i, j, k, r) : error("Magnitude not equal to 1.")
-	Quaternion() = new(0, 0, 0, 1)
-	
-	Quaternion(yaw, pitch, roll) = Quaternion([0 0 sin(yaw / 2) cos(yaw / 2)]) * Quaternion([0 sin(pitch / 2) 0 cos(pitch / 2)]) * Quaternion([sin(roll / 2) 0 0 cos(roll / 2)])
-	
-	function Quaternion(ē, ϕ)
-		if sum(ē) == 0
-			return Quaternion([0 0 0 cos(ϕ / 2)])
-		end
-		dir = normalize(ē) * sin(ϕ / 2)
-		return Quaternion(dir[1], dir[2], dir[3], cos(ϕ / 2))
+	function Elliptic_Orbit(r, a, e)
+		@assert e < 1 "Eccentricity must be less than 1!"
+		new(r, a, e)
+	end
+	function Elliptic_Orbit(r)
+		new(r,r,0) # we'll pretend circular orbits count for this example
 	end
-	
 end
 
 
-# ╔═╡ 639fc5f0-1ab8-4d4e-83b5-77a82ae9bdf8
-q() = Quaternion()
+# ╔═╡ efb58b79-24e4-45c6-ad45-aeaa339d82fd
+ISS = Elliptic_Orbit(420u"km")
 
-# ╔═╡ 37c4a8ef-d503-497a-a63c-3e43d0ebb2a7
-function QuaternionMultiplication(l::Quaternion, r::Quaternion)
-	R = [r.r r.k r.j r.i;
-		 -r.k r.r r.i r.j;
-		 r.j -r.i r.r r.k;
-		 -r.i -r.j -r.k r.r]
-	L = [l.i; l.j; l.k; l.r]
-	return Quaternion(R * L)
-	
+# ╔═╡ 3efd8a29-6a56-4f5c-9cab-0f08875b2064
+function get_velocity(o::Elliptic_Orbit)
+	v = sqrt(μ*(2/o.r - 1/o.a))
+	return v |> u"km/s"
 end
 
-# ╔═╡ 0d67e350-a87e-4a07-a01c-d348f3e62599
-Base.:*(l::Quaternion, r::Quaternion) = QuaternionMultiplication(l::Quaternion, r::Quaternion)
-
-# ╔═╡ cbf7d0fb-855b-442b-80c2-cfb6dcabe104
-begin
-	Base.iterate(q::Quaternion, state=1) = state > 4 ? nothing : (collect(q)[state], state + 1)
-	Base.length(q::Quaternion) = 4
-	Base.collect(q::Quaternion) = [q.i q.j q.k q.r]
-	Base.getindex(q::Quaternion, i) = collect(q)[i]
+# ╔═╡ 59207a25-fa6d-4369-979d-cd9cc2f094cf
+function get_period(o::Elliptic_Orbit)
+	T = 2*π*sqrt(o.a^3/μ)
+	return T |> u"s"
 end
 
-# ╔═╡ 84e6fb12-be8c-4e00-bf9c-d45748347def
-begin
-	LinearAlgebra.norm(q::Quaternion) = norm(collect(q))
-	LinearAlgebra.normalize(q::Quaternion) = collect(q) / norm(q)
-end
+# ╔═╡ 5a4b673b-babb-4e11-a292-d71087fa32bc
 
-# ╔═╡ 2ba455ff-70f5-47d5-9fe8-bf4ebee9386a
-q1 = Quaternion(1,0,0,0)
 
-# ╔═╡ 6895bcb2-9a11-4f0a-b1c2-6640f6fb509c
-q2 = Quaternion([1 2 3], π)
+# ╔═╡ a6c72acc-39fc-4dfc-8126-64c6b35145d1
+get_period(ISS)
 
-# ╔═╡ 045a1898-a3db-4e65-9711-9e4608ce09c6
-q()*q()
+# ╔═╡ d79a6752-77ba-496f-96c3-d9904db0a46b
+get_velocity(ISS)
+
+# ╔═╡ 026321df-6991-4b59-aaba-c467b267a477
+whatsit(u"m")
+
+# ╔═╡ 3955b9d6-7514-4712-ba22-929afda3c77c
+typeof(1.1u"km")
+
+# ╔═╡ a7bacb81-0f19-4d2d-9588-61e912689001
+Elliptic_Orbit(1,2,.9)
+
+# ╔═╡ c3d943b4-809d-4a96-a99d-be7653ba2c8b
 
-# ╔═╡ fafa0a8d-5ae5-49e9-8d11-4abb5748431e
-q1*q2
 
 # ╔═╡ 8924673f-e99c-44b3-be6d-2abf0b2f5e23
 md"""
@@ -1410,16 +1400,18 @@ version = "0.9.1+5"
 # ╟─dc898d32-b30b-4baa-a595-b83ccd1dc86d
 # ╠═9ea4584c-8177-4f69-9739-b2faa93281a8
 # ╠═f43812d2-9f87-489a-9317-e7aa19ffd3bc
+# ╠═f6d87354-ac46-4202-92f8-b39a0db13327
 # ╠═44daff45-f608-47e3-ad6e-fca43532f322
-# ╠═639fc5f0-1ab8-4d4e-83b5-77a82ae9bdf8
-# ╠═37c4a8ef-d503-497a-a63c-3e43d0ebb2a7
-# ╠═0d67e350-a87e-4a07-a01c-d348f3e62599
-# ╠═cbf7d0fb-855b-442b-80c2-cfb6dcabe104
-# ╠═84e6fb12-be8c-4e00-bf9c-d45748347def
-# ╠═2ba455ff-70f5-47d5-9fe8-bf4ebee9386a
-# ╠═6895bcb2-9a11-4f0a-b1c2-6640f6fb509c
-# ╠═045a1898-a3db-4e65-9711-9e4608ce09c6
-# ╠═fafa0a8d-5ae5-49e9-8d11-4abb5748431e
+# ╠═efb58b79-24e4-45c6-ad45-aeaa339d82fd
+# ╠═3efd8a29-6a56-4f5c-9cab-0f08875b2064
+# ╠═59207a25-fa6d-4369-979d-cd9cc2f094cf
+# ╠═5a4b673b-babb-4e11-a292-d71087fa32bc
+# ╠═a6c72acc-39fc-4dfc-8126-64c6b35145d1
+# ╠═d79a6752-77ba-496f-96c3-d9904db0a46b
+# ╠═026321df-6991-4b59-aaba-c467b267a477
+# ╠═3955b9d6-7514-4712-ba22-929afda3c77c
+# ╠═a7bacb81-0f19-4d2d-9588-61e912689001
+# ╠═c3d943b4-809d-4a96-a99d-be7653ba2c8b
 # ╠═8924673f-e99c-44b3-be6d-2abf0b2f5e23
 # ╠═3f7ae2df-9d4d-46d3-b12e-22107a560b66
 # ╠═fbc06121-d53a-4a64-9497-63d7f3583fbb