cycloid_derivation.jl

### A Pluto.jl notebook ###
# v0.19.9

using Markdown
using InteractiveUtils

# ╔═╡ a1c12079-7890-4cc6-bd82-7efe7d73493a
using Symbolics

# ╔═╡ 88a3e8e6-0396-4c4c-9355-a68c8048f23b


# ╔═╡ 6b19d3d6-3462-11ed-1302-632a6139cae2
@variables E R Rᵣ Nₗ Nᵣ ϕ

# ╔═╡ 2a8ac180-b820-4e29-8b50-8e74c635c1d2
@variables Q K ω_I ω_C V_C # These numbers are ones that we will derive

# ╔═╡ 00bd2a07-fde6-4993-9d71-ed6ea050a88f
ω_C ~ K*ω_I

# ╔═╡ 24eb8ebd-1fb6-448f-b1a3-198a9c4e4da4
V_C~E*ω_I

# ╔═╡ 17bb5539-1aeb-4594-9f11-dfcba64c65d2
V_C~-(Q-E)*ω_C~(Q-E)*K*ω_I

# ╔═╡ a0f01496-da93-407b-a59a-fc66cf502a93
K*ω_I*(Q-E)~E*ω_I ~ K*ω_I*Q-K*ω_I*E

# ╔═╡ 00000000-0000-0000-0000-000000000001
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"""

# ╔═╡ Cell order:
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# ╠═24eb8ebd-1fb6-448f-b1a3-198a9c4e4da4
# ╠═17bb5539-1aeb-4594-9f11-dfcba64c65d2
# ╠═a0f01496-da93-407b-a59a-fc66cf502a93
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002