def c6p21():
# Trajectory
def y(theta, x, v0, y0, g=9.8):
return np.tan(theta) * x - (g * x**2) / (2 * v0**2 *
np.cos(theta)**2) + y0
# Constants
v0, x, y0, y1 = 30., 90, 1.8, 1.
deg = (180. / np.pi)
# Args for solution
f = lambda theta: y(theta, x, v0, y0) - y1
return {
'newton_raphson th1': deg * num.newton_raphson(f, 0.4),
'newton_raphson th2': deg * num.newton_raphson(f, 0.9),
'secant_method th1': deg * num.secant_method(f, 0.4, 0.45),
'secant_method th2': deg * num.secant_method(f, 0.9, 0.95)
}
def c6p19():
# Impedance
def z(r, c, l, w):
return np.sqrt( r**(-2) + ( w * c - (w * l)**(-1) )**2 )**(-1)
# Constants
r, c, l, z_desired = 225., 0.6 * 10**(-6), 0.5, 100.
# Args for solution
f = lambda w: z(r, c, l, w) - z_desired
x0, x1, dx = 210, 215, 10**(-4)
return {'newton_raphson': num.newton_raphson( f,x0 ), 'secant_method': num.secant_method( f, x0, x1 ), 'modified_secant': num.modified_secant( f,x1,dx) }
def c6p21():
# Trajectory
def y(theta, x, v0, y0, g=9.8 ):
return np.tan( theta ) * x - (g * x**2) /( 2 * v0**2 * np.cos( theta )**2 ) + y0
# Constants
v0, x, y0, y1 = 30., 90, 1.8, 1.
deg = ( 180. / np.pi )
# Args for solution
f = lambda theta: y( theta, x, v0, y0 ) - y1
return { 'newton_raphson th1': deg * num.newton_raphson( f,0.4 ), 'newton_raphson th2': deg * num.newton_raphson( f, 0.9 ) ,'secant_method th1': deg * num.secant_method(f,0.4, 0.45 ), 'secant_method th2':deg * num.secant_method( f,0.9,0.95 ) }
def c6p19():
# Impedance
def z(r, c, l, w):
return np.sqrt(r**(-2) + (w * c - (w * l)**(-1))**2)**(-1)
# Constants
r, c, l, z_desired = 225., 0.6 * 10**(-6), 0.5, 100.
# Args for solution
f = lambda w: z(r, c, l, w) - z_desired
x0, x1, dx = 210, 215, 10**(-4)
return {
'newton_raphson': num.newton_raphson(f, x0),
'secant_method': num.secant_method(f, x0, x1),
'modified_secant': num.modified_secant(f, x1, dx)
}