Geometrically Exact, Intrinsic Theory for Dynamics of Curved and Twisted Anisotropic Beams

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Flight Dynamics of Highly Flexible Flying Wings (2006, neutral): “2 Structural Model The geometrically-exact, intrinsic equations for the dynamics of a general, non-uniform, twisted, curved, anisotropic beam, undergoing large deformation, are given as F ′ + (k̃ + κ̃)F + f = Ṗ + Ω̃P (1) M ′ + (k̃ + κ̃)M + (ẽ1 + γ̃)F + m = Ḣ + Ω̃H + Ṽ P (2) V ′ + (k̃ + κ̃)V + (ẽ1 + ”
Fundamentals of Structural Stability (2006, background): “Before the energy criterion is justified, let us describe in analytical form the kinetic criterion of stability. This concept was first introduced by Lagrange (1788) for a system with a finite number of degrees of freedom.”
Flight Dynamics of Highly Flexible Aircraft (2008, background): “However, instead of being augmented by the kinematical relations therein, which relate generalized strain and velocity measures to temporal and spatial partial derivatives of displacement and rotation variables, they are augmented by the intrinsic kinematical equations derived in [10].”
Structural and Aerodynamic Models in Nonlinear Flight Dynamics of Very Flexible Aircraft (2010, methodology): “This solution is equivalent to the finite difference solution process proposed by Hodges [24] and results in an energypreserving time integration scheme.”