Julia: apply rotation to ODE solution

Question

I am playing around with the Julia ODE module. I solve a simple Newtonian mechanics equation, involving an inclined plane. For convenience (because I did so when I solved it analytically) I rotate my axes so that e_x follows the plane, and e_y is normal to it. When displaying the solution, though, I'd like to rotate it back so that e_y coincides with the direction of gravity.

Now, pulling out my position vectors from the solution object is not a problem (although my method might not be very idiomatic), nor is plotting them. But doing so, I lose the nice magic that comes with plotting the solution directly. Is there a way to apply my rotation directly to the solution object, so it still behaves like a functor with ready to roll interpolation and the like?

Passing my functions definitions, I run this:

prob = ODEProblem(pfm!, u0, tspan, (g, alpha))
cb = ContinuousCallback(condition, affect!)
sol = solve(prob, Tsit5(), reltol=1e-8, abstol=1e-8, callback=cb)

When plotting sol:

When getting the position vector out before hand with

pos = hcat(sol.u...)[[1, 2], :]

I get

And the not-much-more existing solution after manual rotation with

pos = rot_mat * hcat(sol.u...)[[1, 2], :]

produces