28,840 research outputs found
A general-purpose approach to computer-aided dynamic analysis of a flexible helicopter
A general purpose mathematical formulation is described for dynamic analysis of a helicopter consisting of flexible and/or rigid bodies that undergo large translations and rotations. Rigid body and elastic sets of generalized coordinates are used. The rigid body coordinates define the location and the orientation of a body coordinate frame (global frame) with respect to an inertial frame. The elastic coordinates are introduced using a finite element approach in order to model flexible components. The compatibility conditions between two adjacent elements in a flexible body are imposed using a Boolean matrix, whereas the compatibility conditions between two adjacent bodies are imposed using the Lagrange multiplier approach. Since the form of the constraint equations depends upon the type of kinematic joint and involves only the generalized coordinates of the two participating elements, then a library of constraint elements can be developed to impose the kinematic constraint in an automated fashion. For the body constraints, the Lagrange multipliers yield the reaction forces and torques of the bodies at the joints. The virtual work approach is used to derive the equations of motion, which are a system of differential and algebraic equations that are highly nonlinear. The formulation presented is general and is compared with hard-wired formulations commonly used in helicopter analysis
Discrete second order constrained Lagrangian systems: first results
We briefly review the notion of second order constrained (continuous) system
(SOCS) and then propose a discrete time counterpart of it, which we naturally
call discrete second order constrained system (DSOCS). To illustrate and test
numerically our model, we construct certain integrators that simulate the
evolution of two mechanical systems: a particle moving in the plane with
prescribed signed curvature, and the inertia wheel pendulum with a Lyapunov
constraint. In addition, we prove a local existence and uniqueness result for
trajectories of DSOCSs. As a first comparison of the underlying geometric
structures, we study the symplectic behavior of both SOCSs and DSOCSs.Comment: 17 pages, 6 figure
An influence coefficient method for the application of the modal technique to wing flutter suppression of the DAST ARW-1 wing
The methods used to compute the mass, structural stiffness, and aerodynamic forces in the form of influence coefficient matrices as applied to a flutter analysis of the Drones for Aerodynamic and Structural Testing (DAST) Aeroelastic Research Wing. The DAST wing was chosen because wind tunnel flutter test data and zero speed vibration data of the modes and frequencies exist and are available for comparison. A derivation of the equations of motion that can be used to apply the modal method for flutter suppression is included. A comparison of the open loop flutter predictions with both wind tunnel data and other analytical methods is presented
Nonholonomic Dynamics
Nonholonomic systems are, roughly speaking, mechanical
systems with constraints on their velocity
that are not derivable from position constraints.
They arise, for instance, in mechanical systems
that have rolling contact (for example, the rolling
of wheels without slipping) or certain kinds of sliding
contact (such as the sliding of skates). They are
a remarkable generalization of classical Lagrangian
and Hamiltonian systems in which one allows position
constraints only.
There are some fascinating differences between
nonholonomic systems and classical Hamiltonian
or Lagrangian systems. Among other things: nonholonomic
systems are nonvariational—they arise
from the Lagrange-d’Alembert principle and not
from Hamilton’s principle; while energy is preserved
for nonholonomic systems, momentum is
not always preserved for systems with symmetry
(i.e., there is nontrivial dynamics associated with
the nonholonomic generalization of Noether’s
theorem); nonholonomic systems are almost Poisson
but not Poisson (i.e., there is a bracket that together
with the energy on the phase space defines
the motion, but the bracket generally does not satisfy
the Jacobi identity); and finally, unlike the
Hamiltonian setting, volume may not be preserved
in the phase space, leading to interesting asymptotic
stability in some cases, despite energy conservation.
The purpose of this article is to engage
the reader’s interest by highlighting some of these
differences along with some current research in the
area. There has been some confusion in the literature
for quite some time over issues such as the
variational character of nonholonomic systems, so
it is appropriate that we begin with a brief review
of the history of the subject
Covariant Balance Laws in Continua with Microstructure
The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of
energy method to continua with microstructure. The key idea is to replace the
group of Galilean transformations with the group of diffeomorphisms of the
ambient space. A key advantage is that one obtains in a natural way all the
needed balance laws on both the macro and micro levels along with two
Doyle-Erickson formulas
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