initial commit

.gitignore

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+.vscode/

Manifest.toml

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+# This file is machine-generated - editing it directly is not advised
+
+julia_version = "1.8.2"
+manifest_format = "2.0"
+project_hash = "edef2709ca5ed93a887579907c4eb7045e5446ec"
+
+[[deps.Artifacts]]
+uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
+
+[[deps.CompilerSupportLibraries_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
+version = "0.5.2+0"
+
+[[deps.Libdl]]
+uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
+
+[[deps.LinearAlgebra]]
+deps = ["Libdl", "libblastrampoline_jll"]
+uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+
+[[deps.OpenBLAS_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
+uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
+version = "0.3.20+0"
+
+[[deps.Random]]
+deps = ["SHA", "Serialization"]
+uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+
+[[deps.SHA]]
+uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
+version = "0.7.0"
+
+[[deps.Serialization]]
+uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
+
+[[deps.SparseArrays]]
+deps = ["LinearAlgebra", "Random"]
+uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+
+[[deps.StaticArrays]]
+deps = ["LinearAlgebra", "Random", "StaticArraysCore", "Statistics"]
+git-tree-sha1 = "f86b3a049e5d05227b10e15dbb315c5b90f14988"
+uuid = "90137ffa-7385-5640-81b9-e52037218182"
+version = "1.5.9"
+
+[[deps.StaticArraysCore]]
+git-tree-sha1 = "6b7ba252635a5eff6a0b0664a41ee140a1c9e72a"
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+
+[[deps.Statistics]]
+deps = ["LinearAlgebra", "SparseArrays"]
+uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+
+[[deps.libblastrampoline_jll]]
+deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
+uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
+version = "5.1.1+0"

Project.toml

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+name = "Inertia"
+uuid = "58d22092-de16-4bdf-bc5b-1f5634c2cdd0"
+authors = ["tom <tomrottier@hotmail.com>"]
+version = "0.1.0"
+
+[deps]
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"

src/Inertia.jl

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+module Inertia
+
+using LinearAlgebra, StaticArrays
+
+include("solids.jl")
+include("composite.jl")
+
+export Cuboid, Sphere, Cylinder
+export centre_of_mass, calculate_inertia
+
+
+end # module Inertia

src/composite.jl

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+# calculate inertial properties for combinations of solids
+
+# inertia about axes rotated by R from axes inertia currently expressed in
+rotated_inertia(I, R) = R * I * R'
+
+# parallel axis theorem for inertia tensor about a point p from CoM
+function parallel_axis(I, m, p)
+    Ixx = I[1, 1] + m * (p[2]^2 + p[3]^2)
+    Iyy = I[2, 2] + m * (p[1]^2 + p[3]^2)
+    Izz = I[3, 3] + m * (p[1]^2 + p[2]^2)
+    Ixy = Iyx = I[1, 2] - m * p[1] * p[2]
+    Ixz = Izx = I[1, 3] - m * p[1] * p[3]
+    Iyz = Izy = I[2, 3] - m * p[2] * p[3]
+
+    return [Ixx Ixy Ixz; Iyx Iyy Iyz; Izx Izy Izz]
+end
+
+parallel_axis(solid::AbstractSolid, p) = parallel_axis(solid.moi, solid.mass, p)
+
+# sum inertia
+sum_inertia(I...) = sum(I)
+
+# centre of mass
+centre_of_mass(ms, rs) = reduce(+, ms .* rs) / sum(ms)
+
+centre_of_mass(solids::Vector{AbstractSolid}, rs) = centre_of_mass(getfield.(solids, :mass), rs)
+
+# calculate total inertia of collection of solids about a point p
+function calculate_inertia(Is, Rs, ms, rs, p)
+    # total inertia about CoM
+    Itotal = zeros(3, 3)
+
+    for (I, R, m, r) in zip(Is, Rs, ms, rs)
+        # inertia about axes parallel to global frame
+        I′ = R * I * R'
+
+        # inertia about com
+        I′cm = parallel_axis(I′, m, p - r)
+
+        Itotal += I′cm
+    end
+
+    return Itotal
+end
+
+# total inertia about CoM
+calculate_inertia(Is, Rs, ms, rs) = calculate_inertia(Is, Rs, ms, rs, centre_of_mass(ms, rs))
+
+calculate_inertia(solids::Vector{AbstractSolid}, Rs, rs, p) = begin
+    calculate_inertia(getfield.(solids, :moi), Rs, getfield.(solids, :mass), rs, p)
+end

src/solids.jl

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+# regular solids and their inertial properties
+abstract type AbstractSolid end
+
+## cuboid
+struct Cuboid{T} <: AbstractSolid
+    length::T
+    width::T
+    height::T
+    mass::T
+    moi::SMatrix{3,T} # principle inertia tensor
+
+    # determine moment of inertia from dimensions and mass
+    function Cuboid{T}(l, w, h, m) where {T}
+        c = 1 / 12 * m
+        I = @SMatrix [c*(w^2+h^2) 0 0; 0 c*(l^2+h^2) 0; 0 0 c*(l^2+w^2)]
+
+        return new{T}(l, w, h, m, I)
+    end
+end
+
+## sphere
+struct Sphere{T} <: AbstractSolid
+    radius::T
+    mass::T
+    moi::SMatrix{3,T} # principle inertia tensor
+
+    # determine moment of inertia from dimensions and mass
+    function Sphere{T}(r, m) where {T}
+        c = 2 / 5 * m
+        I = @SMatrix [c*r^2 0 0; 0 c*r^2 0; 0 0 c*r^2]
+
+        return new{T}(r, m, I)
+    end
+end
+
+## cylinder
+struct Cylinder{T} <: AbstractSolid
+    radius::T
+    length::T
+    mass::T
+    moi::SMatrix{3,T} # principle inertia tensor
+
+    # determine moment of inertia from dimensions and mass
+    function Cylinder{T}(r, l, m) where {T}
+        c1 = 1 / 12 * m
+        c2 = 1 / 2 * m
+        I = @SMatrix [c2*r^2 0 0; 0 c1*(3r^2+l^2) 0; 0 0 c1*(3r^2+l^2)]
+
+        return new{T}(r, l, m, I)
+    end
+end
+
+