Problem 3 Consider the general system of second order autonomus nonlinear ODEs M(q)q + c(q, q) = Q(q, q, u) Here M (q) is a n xn square matrix function, q is the vector of generalized coordinates, c(q, q) is a column vector that is quadratic in generalized velocities, q, u is the control vector. It is assumed that all functions (M(q), c(q, q), Q(q, q, u)) are defined on domains in the real spaces of their variables (e.g. M(q) is defined on a domain D, C R", etc.) Can you always convert this to the generic first order form, x = f(x, u)? If conditions are necessary write them down and write r and f(x, u). If all the functions (M (q), c(q, q), Q(q, q, u)) are continous on their domains of definition and the first order form can be created what can be stated about f(x, u)