The concept of an elastica was first put forward by Bernoulli in the 17th century and extended by Euler in 1744. The concept of an elastica refers to the modelling of a thin wire-like structure by an elastic curve, the elastica, capable of non-linear large-scale deflections and rotations. The solution for the curve of the elastica is particularly useful in studying buckling and other related stability problems. Its formulation in a plane involves two geometrical constraint equations, two equations for the force equilibrium in two orthogonal directions, an equation for the moment equilibrium and a final constitutive equation relating the applied bending moment to the slope (Plaut and Virgin, 2009). In this example, we shall apply the elastica to a control problem with a number of practical applications. Consider a uniform, thin, flexible, inextensible, elastic strip, with length S, bending rigidity EI, crosssectional area A, mass per unit length m, weight per unit length mg and mass moment of inertia J. The elastric strip is assumed to be incapable of being deformed in shear. The effect of weight, transverse and axial inertia forces and rotary inertia are considered in the formulation. Only the in-plane motion is considered, while all damping is neglected. To define the geometry of the elastica, the height of the strip is assumed to be H and the arc length of a typical mass point from the left end is assumed to be s. The horizontal and vertical coordinates of a typical mass point are assumed to be x(s, t) and y(s, t), respectively, while the angle of rotation is assumed to be θ(s, t), where t is the time. The angle with the horizontal at s = 0 is denoted by α. The bending moment M(s,t) is assumed to be positive if it is counter-clockwise on a positive face. The horizontal force P(s, t) is assumed to be positive in compression, while the vertical force Q(s,t) is positive if it is downward on a positive face.