Abstract
This note provides a direct method for obtaining Lagrange’s equations describing the rotational motion of a rigid body in terms of quaternions by using the so-called fundamental equation of constrained motion.
Highlights
In this note, a general formulation for rigid body rotational dynamics is developed using quaternions, known as Euler parameters
The equations of rotational motion in terms of quaternions appear to have been first obtained by Nikravesh et al ͓1͔
The authors in this particular paper developed an approach to model and simulate constrained mechanical systems in which the componentsbodiesin the mechanical system are connected by nonredundant holonomic constraints
Summary
A general formulation for rigid body rotational dynamics is developed using quaternions, known as Euler parameters. The equations of rotational motion in terms of quaternions appear to have been first obtained by Nikravesh et al ͓1͔ The authors in this particular paper developed an approach to model and simulate constrained mechanical systems in which the componentsbodiesin the mechanical system are connected by nonredundant holonomic constraints. Morton2͔ obtains both Hamilton’s and Lagrange’s equations in terms of quaternions Neither of these sets of equations is developed solely through the use of Hamiltonian or Lagrangian dynamics, as one might have expected. He obtains, through this somewhat long and involved procedure, the crucial connection between the physically applied torque vector and the generalized quaternion torques that are necessary to complete his Hamilton’s equations. To formulate the equations of motion of the rotating rigid body, which may be subjected to a generalized torque four-vector ⌫upart of which may be derived from a potential, we begin by considering its kinetic energy
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