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#!/Applications/Julia-1.8.app/Contents/Resources/julia/bin/julia
using Plots # for plotting trajectory
g = 9.8 # acceleration of gravity in m/s^2
dt = 0.01 # time step in seconds
t_final = 1.0 # final time of trajectory
steps = Int64(t_final/dt) # number of time steps
y = zeros(steps+1) # initial array of heights in meters
v = zeros(steps+1) # initial array of velocities in m/s
function dynamics!(y, v, t::Float64) # ! notation tells us that arguments will be modified
for i in 1:steps
y[i+1] = y[i] + v[i] * dt
v[i+1] = v[i] - g * dt
#y[i+1] = y[i] + 0.5 * (v[i] + v[i+1]) * dt
t = t + dt
end
return t
end
y0 = 10.0 # initial position in meters
v0 = 0.0 # initial velocity in m/s
y[1] = y0
v[1] = v0
t = dynamics!(y, v, 0.0) # evolve forward in time
println("\n\t Results")
println("final time = ", t)
println("y = ", y[steps+1], " and v = ", v[steps+1])
println("exact v = ", v0 - g * t)
println("exact y = ", y0 + v0 * t - 0.5 * g * t^2.0)
plot(y) # plot position as a function of time
# energy = g * y + 0.5 * v .* v # here the mass = 1
# println("initial energy = ", energy[1])
# println("final energy = ", energy[steps+1])
# plot(energy)
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