How to present (x(t))'', (θ(t))'' in symbolic version matlab?
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Matthew Worker on 6 Feb 2023
There are six equations below (M, m, g, b, L, J are constant):
M*(x(t))'' = F(t) - N(t) - b*(x(t))'
J*(θ(t))'' = P(t)*sin(θ(t))*(L/2) - N(t)*cos(θ(t))*(L/2)
m*(xp(t))'' = N(t)
m*(yp(t))'' = P(t) - mg
xp(t) = x(t) +(L/2)*sin(θ(t))
yp(t) = (L/2)*cos(θ(t))
I want to combine and simplify these 6 symbolic equations into 2 symbolic euqations only presented by x(t), θ(t) and F(t).
However, I do not know how to show the (x(t))'', (θ(t))'' in symbolic version. Can anyone help me with it?
Walter Roberson on 6 Feb 2023
syms b J g L M m
syms F(t) N(t) P(t) theta(t) x(t) xp(t) yp(t)
x_prime = diff(x);
x_dprime = diff(x_prime);
theta_prime = diff(theta)
theta_dprime = diff(theta_prime);
xp_prime = diff(xp);
xp_dprime = diff(xp_prime);
yp_prime = diff(yp);
yp_dprime = diff(yp_prime);
eqn1 = M*xp_dprime == F - N - b*x_prime
eqn2 = J*theta_dprime == P*sin(theta)*(L/2) - N * cos(theta)*(L/2)
eqn3 = m*xp_dprime == N
eqn4 = m*yp_dprime == P - m*g
eqn5 = xp == x + (L/2)*sin(theta)
eqn6 = yp == (L/2)*cos(theta)