do hw2

1 files changed, 91 insertions, 0 deletions

diff --git a/hw2/2-18.jl b/hw2/2-18.jl
new file mode 100644
index 0000000..58bad47
--- /dev/null
+++ b/hw2/2-18.jl
@@ -0,0 +1,91 @@
+using Plots # for plotting trajectory
+
+# simulation parameters
+Δt = 0.001 # time step
+x_max = 60.0 # in feet
+v_0 = 95.0 # mph
+v_0 = v_0 * 5280 / 3600 # convert mph to feet/s
+y_0 = 6.0 # in feet
+ω = 0.0 # in rad/s
+m = 149 # in grams
+S_0_over_m = 4.1 * 10^(-4) # unitless
+B_ref_over_m = 4.0 * 10^(-5) # in m-1, at 300K
+g = 32.2 # in ft/s^2
+
+function dynamics!(
+    x::Vector{Float64}, y::Vector{Float64}, 
+    v_y::Vector{Float64}, v_x::Vector{Float64}, 
+    t::Vector{Float64}) 
+    while x[end] <= x_max
+        # decompose previous positions and velocities 
+        x_i = x[end]
+        y_i = y[end]
+        v_x_i = v_x[end]
+        v_y_i = v_y[end]
+
+        # calculate new positions
+        x_new = x_i + v_x_i * Δt
+        y_new = y_i + v_y_i * Δt
+
+        # calculate drag force
+        v_i = sqrt(v_x_i^2 + v_y_i^2)
+        F_x = - B_ref_over_m * v_x_i * v_i
+        F_y = - g + S_0_over_m * v_x_i * ω
+
+        # calculate new velocities
+        v_x_new = v_x_i + F_x * Δt
+        v_y_new = v_y_i + F_y * Δt
+
+        # store new positions and velocities
+        push!(x, x_new)
+        push!(y, y_new)
+        push!(v_x, v_x_new)
+        push!(v_y, v_y_new)
+        push!(t, t[end] + Δt)
+    end
+end
+
+# interpolate the last point that's past the x_max
+function interpolate!(x::Vector{Float64}, y::Vector{Float64})
+    if x[end] <= x_max
+        return
+    end
+
+    x_i = x[end-1]
+    y_i = y[end-1]
+
+    x_f = x[end]
+    y_f = y[end]
+
+    m = (y_f - y_i) / (x_f - x_i)
+    b = y_i - m * x_i
+    
+    x_new = x_max
+    y_new = m * x_new + b
+
+    x[end] = x_new
+    y[end] = y_new
+end
+
+# run the simulation with ω = 0
+x = [0.0]
+y = [y_0]
+v_x = [v_0] # pitch only in x direction
+v_y = [0.0]
+t = [0.0]
+dynamics!(x, y, v_y, v_x, t)
+interpolate!(x, y)
+plot(x, y, label="ω = 0", xlabel="x (feet)", ylabel="y (feet)", lw=2, title="Trajectory of a Fastball with Backspin")
+println("y-value at x_max (60ft) for ω = 0:\t", y[end], " feet")
+
+# run the simulation with ω = 1000 rpm
+ω = 1000 * 2 * π / 60 # convert rpm to rad/s
+x = [0.0]
+y = [y_0]
+v_x = [v_0] # pitch only in x direction
+v_y = [0.0]
+t = [0.0]
+dynamics!(x, y, v_y, v_x, t)
+interpolate!(x, y)
+println("y-value at x_max (60ft) for ω = 1000 rpm:\t", y[end], " feet")
+plot!(x, y, label="ω = 1000 rpm", lw=2)