@@ -27,7 +27,7 @@ We solve the ODE system on the sphere ``\mathbb S^2`` given by
2727```
2828
2929``` julia
30- using ManifoldDiffEq, Manifolds
30+ using ManifoldDiffEq, Manifolds, LieGroups
3131using GLMakie, LinearAlgebra, Colors
3232
3333n = 25
@@ -59,6 +59,7 @@ arr = GLMakie.arrows!(
5959)
6060save (" docs/src/assets/img/first_example_vector_field.png" , f)
6161```
62+
6263which looks like
6364
6465![ The ODE illustrated as a tangent vector field] ( assets/img/first_example_vector_field.png )
@@ -73,7 +74,7 @@ u0 = [0.0, sqrt(9/10), sqrt(1/10)]
7374tspan = (0 , 20.0 )
7475
7576A_lie = LieManifoldDiffEqOperator {Float64} () do u, p, t
76- return hat (SpecialOrthogonal (3 ), Matrix (I (3 )), cross (u, f2 (u... )))
77+ return hat (SpecialOrthogonalGroup (3 ), Matrix (I (3 )), cross (u, f2 (u... )))
7778end
7879prob_lie = ManifoldODEProblem (A_lie, u0, tspan, S2)
7980
@@ -82,9 +83,9 @@ A_frozen = FrozenManifoldDiffEqOperator{Float64}() do u, p, t
8283end
8384prob_frozen = ManifoldODEProblem (A_frozen, u0, tspan, S2)
8485
85- action = RotationAction ( Euclidean ( 3 ), SpecialOrthogonal (3 ))
86- alg_lie_euler = ManifoldDiffEq. ManifoldLieEuler (S2, ExponentialRetraction (), action)
87- alg_lie_rkmk4 = ManifoldDiffEq. RKMK4 (S2, ExponentialRetraction (), action)
86+ action = GroupAction ( LeftMultiplicationGroupAction ( ), SpecialOrthogonalGroup (3 ), S2 )
87+ alg_lie_euler = ManifoldDiffEq. ManifoldLieEuler (ExponentialRetraction (), action)
88+ alg_lie_rkmk4 = ManifoldDiffEq. RKMK4 (ExponentialRetraction (), action)
8889
8990alg_manifold_euler = ManifoldDiffEq. ManifoldEuler (S2, ExponentialRetraction ())
9091alg_cg2 = ManifoldDiffEq. CG2 (S2, ExponentialRetraction ())
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