Add solar system test for Lagrangian system.

Project.toml

@@ -18,8 +18,9 @@ Symbolics = "5.24"
 julia = "1.10"
 
 [extras]
+Parameters = "d96e819e-fc66-5662-9728-84c9c7592b0a"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["SafeTestsets", "Test"]
+test = ["Parameters", "SafeTestsets", "Test"]

test/lagrangian_solar_system.jl

@@ -0,0 +1,163 @@
+using EulerLagrange
+using GeometricEquations
+using LinearAlgebra
+using Parameters
+using Test
+
+
+const tspan = (0.0, 3)
+const tstep = 0.5
+
+const G = 2.95912208286e-4
+
+#Sun
+const m₁ =  1.0
+const q₁ = [0., 0., 0.]
+const q̇₁ = [0., 0., 0.]
+const p₁ = [0., 0., 0.]
+
+#Jupiter
+const m₂ = 0.000954786104043 
+const q₂ = [-3.5023653, -3.8169847, -1.5507963]
+const q̇₂ = [0.00565429, -0.0041249, -0.00190589]
+const p₂ = m₂*q̇₂
+
+#Saturn 
+const m₃ = 0.000285583733151
+const q₃ = [9.0755314,-3.0458353,-1.6483708]
+const q̇₃ = [0.00168318,0.00483525,0.00192462]
+const p₃  = m₃ * q̇₃ 
+
+#Uranus
+const m₄ = 0.0000437273164546
+const q₄ = [8.3101420,-16.2901086,-7.2521278]
+const q̇₄ = [0.00354178,0.00137102,0.00055029]
+const p₄ = m₄*q̇₄
+
+#Neptune
+const m₅ = 0.0000517759138449
+const q₅ = [11.4707666,-25.7294829,-10.8169456]
+const q̇₅ = [0.00288930,0.00114527,0.00039677]
+const p₅ = m₅*q̇₅
+
+#Pluto
+const m₆ = 1/(1.3e8)
+const q₆ = [-15.5387357,-25.2225594,-3.1902382]
+const q̇₆ = [0.00276725,-0.00170702,-0.00136504]
+const p₆ = m₆*q̇₆
+
+# 2d System
+const ss2 = (
+    d = 3,
+    n = 2,
+    m = [m₁,m₂],
+    t₀ = 0.0,
+    q₀ = [q₁; q₂],
+    v₀ = [q̇₁; q̇₂],
+    p₀ = [p₁; p₂],
+    default_parameters = (
+        d = 3,
+        n = 2,
+        G = 2.95912208286e-4,
+        m = [m₁,m₂]
+    )
+)
+
+# 6d System
+const ss6 = (
+    d = 3,
+    n = 6,
+    m = [m₁,m₂,m₃,m₄,m₅,m₆],
+    t₀ = 0.0,
+    q₀ = [q₁; q₂; q₃; q₄; q₅; q₆],
+    v₀ = [q̇₁; q̇₂; q̇₃; q̇₄; q̇₅; q̇₆],
+    p₀ = [p₁; p₂; p₃; p₄; p₅; p₆],
+    default_parameters = (
+        d = 3,
+        n = 6,
+        G = 2.95912208286e-4,
+        m = [m₁,m₂,m₃,m₄,m₅,m₆]
+    )    
+)
+
+
+function v̄(v,t,q,p,params)
+    p = transpose(reshape(p, params.d, params.n))
+    v .= reshape(transpose(p ./ params.m), params.d * params.n)
+    nothing
+end
+
+function p̃(p,t,q,v,params)
+    v = transpose(reshape(v, params.d, params.n))
+    p .= reshape(transpose(v .* params.m), params.d * params.n)
+    nothing
+end
+
+function hamiltonian(t, q, p, params, d, n)
+    @unpack G, m = params
+
+    q = transpose(reshape(q, d, n))
+    p = transpose(reshape(p, d, n))
+
+    H = zero(eltype(q))
+    for i in 1:n
+        H += 1/2 / m[i] * p[i,:] ⋅ p[i,:]
+        for j in 1:i-1
+            H -= G*(m[i]*m[j]) / norm(q[i,:]-q[j,:])
+        end
+    end
+
+    return H
+end
+
+
+function lagrangian(t, q, v, params, d, n)
+    @unpack G, m = params
+
+    q = transpose(reshape(q, d, n))
+    v = transpose(reshape(v, d, n))
+
+    L = zero(eltype(q))
+    for i in 1:n
+        L += 1/2 * m[i] * v[i,:] ⋅ v[i,:]
+        for j in 1:i-1
+            L += G*(m[i]*m[j]) / norm(q[i,:]-q[j,:])
+        end
+    end
+
+    return L
+end
+
+
+
+function test_solar_system(ss)
+    @unpack d, n, m, t₀, q₀, v₀, p₀ = ss
+    params = ss.default_parameters
+
+    # Symbolic variables and parameters
+    t, x, v = lagrangian_variables(d*n)
+    sparams = symbolize(params)
+
+    # LagrangianSystem
+    lag_sys = LagrangianSystem(lagrangian(t, x, v, sparams, d, n), t, x, v, sparams; dosimplify = false)
+
+    p₁, p₂ = zero(p₀), zero(p₀)
+    ṗ₁, ṗ₂ = zero(p₀), zero(p₀)
+
+    eqs = functions(lag_sys)
+
+    eqs.ϑ(p₁, t₀, q₀, v₀, params)
+    eqs.f(ṗ₁, t₀, q₀, v₀, params)
+
+    p̃(p₂, t₀, q₀, v₀, params)
+    # f̃(ṗ₂, t₀, q₀, v₀, params)
+
+    @test eqs.L(t₀, q₀, v₀, params) == lagrangian(t₀, q₀, v₀, params, d, n)
+    @test p₁ ≈ p₂  atol=2eps()
+    # @test ṗ₁ ≈ ṗ₂  atol=2eps()
+
+end
+
+
+test_solar_system(ss2)
+test_solar_system(ss6)

test/lagrangian_tests.jl

@@ -1,3 +1,4 @@
 @safetestset LagrangianGeneral = "$(rpad("General Functionality",80))" begin include("lagrangian_general.jl") end
 @safetestset LagrangianParticle = "$(rpad("Particle in square potential",80))" begin include("lagrangian_particle.jl") end
 @safetestset LagrangianLotkaVolterra = "$(rpad("Lotka-Volterra",80))" begin include("lagrangian_lotka_volterra.jl") end
+@safetestset LagrangianSolarSystem = "$(rpad("Solar System",80))" begin include("lagrangian_solar_system.jl") end