Generalise degenerate Lagrangians.

src/lagrangian_degenerate.jl

@@ -10,7 +10,7 @@ struct DegenerateLagrangianSystem
     equations
     functions
 
-    function DegenerateLagrangianSystem(θ, H, t, x, v, params = NamedTuple())
+    function DegenerateLagrangianSystem(K, H, t, x, v, params = NamedTuple())
 
         @assert eachindex(x) == eachindex(v)
 
@@ -27,11 +27,10 @@ struct DegenerateLagrangianSystem
 
         ẋ  = collect(Dt.(x))
 
-        K  = θ ⋅ v
         L  = K - H
         EL = [expand_derivatives(Dx[i](L) - Dt(Dv[i](L))) for i in eachindex(Dx,Dv)]
         ∇H = [expand_derivatives(dx(H)) for dx in Dx]
-        ϑ  = [expand_derivatives(dv(L)) for dv in Dv]
+        ϑ  = [expand_derivatives(dv(K)) for dv in Dv]
         f  = [expand_derivatives(dx(L)) for dx in Dx]
         u  = [u for u in ẋ]
         g  = [expand_derivatives(Dt.(ϑ))]

test/lagrangian_lotka_volterra.jl

@@ -3,9 +3,10 @@ using LinearAlgebra
 using Test
 
 
-H(t, x, v, params) = params.a₁ * x[1] + params.a₂ * x[2] + params.b₁ * log(x[1]) + params.b₂ * log(x[2])
-L(t, x, v, params) = log(x[2]) / x[1] / 2 * v[1] - log(x[1]) / x[2] / 2 * v[2] - H(t,x,v,params)
 ϑ(t, x, v, params) = [log(x[2]) / x[1] / 2, - log(x[1]) / x[2] / 2]
+H(t, x, v, params) = params.a₁ * x[1] + params.a₂ * x[2] + params.b₁ * log(x[1]) + params.b₂ * log(x[2])
+K(t, x, v, params) = ϑ(t, x, v, params) ⋅ v
+L(t, x, v, params) = K(t, x, v, params) - H(t,x,v,params)
 
 dHd₁(t, q, params) = params.a₁ + params.b₁ / q[1]
 dHd₂(t, q, params) = params.a₂ + params.b₂ / q[2]
@@ -93,7 +94,7 @@ f̃(ṗ₂, t₀, q₀, v₀, params)
 
 # DegenerateLagrangianSystem
 
-deg_lag_sys = DegenerateLagrangianSystem(ϑ(t,x,v,sparams), H(t,x,v,sparams), t, x, v, sparams)
+deg_lag_sys = DegenerateLagrangianSystem(K(t,x,v,sparams), H(t,x,v,sparams), t, x, v, sparams)
 
 q̇₁, q̇₂ = zero(q₀), zero(q₀)
 p₁, p₂ = zero(p₀), zero(p₀)