Rotation-electronic interaction in the 3p-complex Rydberg state of water

An energy theory is formulated for the rotational energy levels in a p-complex Rydberg state of an asymmetric top molecule of symmetry C2v. The effective Hamiltonian used consists of the usual rigid rotor Hamiltonian augmented with terms representing electronic spin and orbital angular momentum effects. Criteria for assigning symmetry species to the rotational energy levels, following Houganfs scheme that uses the full molecular group,are established and given in the form of a table. This is particularly suitable when eigenvectors are calculated on a digital computer. Also, an intensity theory for transitions to the Rydberg p-complex singlet states is presented and selection rules in terms of symmetry species of energy states are established. Finally, applications to HpO and DpO are given.

Spacecraft's attitude prediction: solar radiation torque and the Earth's shadow

A semi-analytical approach is proposed to study the rotational motion of an artificial satellite, under the influence of torque due to the solar radiation pressure, and taking into account the influence of Earth's shadow. Using Andoyer variables the equations for the rotational motion are presented in extended Hamiltonian form. In order to get a solution for the state variables close to an actual motion, the considered model for the shadow function takes into account physical and geometric factors and three specific regions: shadow, penumbra and full light. A mapping for the shadow function is proposed and a semi-analytical process is applied. When the satellite is totally illuminated or it is inside the penumbra, a known analytical solution is used to compute the satellite's attitude. A numerical simulation shows, when the penumbra region is included, the attenuation of the rotational motion during the transition from the shadow to the illuminate region and vice versa. (c) 2005 Published by Elsevier Ltd on behalf of COSPAR.

Analytical attitude prediction of spin stabilized spacecrafts perturbed by magnetic residual torque

An analytical approach for spin-stabilized spacecraft attitude prediction is presented for the influence of the residual magnetic torques. Assuming an inclined dipole model for the Earth's magnetic field, an analytical averaging method is applied to obtain the mean residual torque every orbital period. The orbit mean anomaly is utilized to compute the average components of residual torque in the spacecraft body frame reference system. The theory is developed for time variations in the orbital elements, and non-circular orbits, giving rise to many curvature integrals. It is observed that the residual magnetic torque does not have component along the spin axis. The inclusion of this torque on the rotational motion differential equations of a spin stabilized spacecraft yields conditions to derive an analytical solution. The solution shows that residual torque does not affect the spin velocity magnitude, contributing only for the precession and the drift of the spin axis of the spacecraft. (c) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

Attitude propagation using non-singular canonical variables

Three sets of non-singular canonical variables for the rotational motion are analyzed. These sets are useful when the angle between z-axis of a coordinate system fixed in artificial satellite ( here defined by the directions of principal moments of inertia of the satellite) and the rotational angular momentum vector is zero or when the angle between Z-inertial axis and rotational angular momentum vector is zero. The goal of this paper is to compare all these sets and to determine the benefits of their uses. With this objective, the dynamical equations of each set were derived, when mean hamiltonian associate with the gravity gradient torque is included. For the torque-free rotational motion, analytical solutions are computed for symmetrical satellite for each set of variables. When the gravity gradient torque is included, an analytical solution is shown for one of the sets and a numerical solution is obtained for one of the other sets. By this analysis we can conclude that: the dynamical equation for the first set is simple but it has neither clear geometrical nor physical meaning; the other sets have geometrical and physical meaning but their dynamical equations are more complex.

Nonlinear dynamic model and simulation of morphing wing profile actuated by shape memory alloys

Morphing aircraft have the ability to actively adapt and change their shape to achieve different missions efficiently. The development of morphing structures is deeply related with the ability to model precisely different designs in order to evaluate its characteristics. This paper addresses the dynamic modeling of a sectioned wing profile (morphing airfoil) connected by rotational joints (hinges). In this proposal, a pair of shape memory alloy (SMA) wires are connected to subsequent sections providing torque by reducing its length (changing airfoil camber). The dynamic model of the structure is presented for one pair of sections considering the system with one degree of freedom. The motion equations are solved using numerical techniques due the nonlinearities of the model. The numerical results are compared with experimental data and a discussion of how good this approach captures the physical phenomena associated with this problem. © The Society for Experimental Mechanics, Inc. 2012.

Spin stabilized satellite's attitude propagation with quaternions

This paper presents a study of a modeling scheme for the spin stabilized satellites attitude, entirely developed in terms of quaternion parametrization. The analysis includes numerical propagation of the rotational motion equation, considering the influence of the following torques: aerodynamic, gravity gradient, residual magnetic, eddy currents and the one due to the Lorentz force. Applications are developed considering the Brazilian Spin Stabilized Satellites SCD1 and SCD2, which are quite appropriated for verification and comparison of the theory with the real data generated and processed by the INPE's Satellite Control Center (SCC). The results show that for SCD1 and SCD2 the influence of the eddy current torque is bigger than the others ones, not only due to the orbit altitude, but also to other specific satellites characteristics. The influence of the torque due to Lorentz force is smaller than the others ones because of the dimension and the electrical charges of the SCD1 and SCD2. In all performed tests the errors remained within the dispersion range specified for the attitude determination system of INPE's SCC. The results show the feasibility of using the quaternion attitude parametrization for modeling the satellite dynamics of spin stabilized satellites.

Non-Markovian expansion in quantum Brownian motion

We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion. We present detailed results for the free and the quadratic cases, which can be compared to exact solutions to test the convergence of the method, and discuss potentials of a general nonlinear form. © 2013 Elsevier B.V. All rights reserved.

Measurement of the rotational inertia of bodies by using mechanical spectroscopy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Design and Characterization of Curved and Spherical Flexure Hinges for Planar and Spatial Compliant Mechanisms

A flexure hinge is a flexible connector that can provide a limited rotational motion between two rigid parts by means of material deformation. These connectors can be used to substitute traditional kinematic pairs (like bearing couplings) in rigid-body mechanisms. When compared to their rigid-body counterpart, flexure hinges are characterized by reduced weight, absence of backlash and friction, part-count reduction, but restricted range of motion. There are several types of flexure hinges in the literature that have been studied and characterized for different applications. In our study, we have introduced new types of flexures with curved structures i.e. circularly curved-beam flexures and spherical flexures. These flexures have been utilized for both planar applications (e.g. articulated robotic fingers) and spatial applications (e.g. spherical compliant mechanisms). We have derived closed-form compliance equations for both circularly curved-beam flexures and spherical flexures. Each element of the spatial compliance matrix is analytically computed as a function of hinge dimensions and employed material. The theoretical model is then validated by comparing analytical data with the results obtained through Finite Element Analysis. A case study is also presented for each class of flexures, concerning the potential applications in the optimal design of planar and spatial compliant mechanisms. Each case study is followed by comparing the performance of these novel flexures with the performance of commonly used geometries in terms of principle compliance factors, parasitic motions and maximum stress demands. Furthermore, we have extended our study to the design and analysis of serial and parallel compliant mechanisms, where the proposed flexures have been employed to achieve spatial motions e.g. compliant spherical joints.

Accurate rotational constant and bond lengths of hexafluorobenzene by femtosecond rotational Raman coherence spectroscopy and ab initio calculations

The gas-phase rotational motion of hexafluorobenzene has been measured in real time using femtosecond (fs) time-resolved rotational Raman coherence spectroscopy (RR-RCS) at T = 100 and 295 K. This four-wave mixing method allows to probe the rotation of non-polar gas-phase molecules with fs time resolution over times up to ∼5 ns. The ground state rotational constant of hexafluorobenzene is determined as B 0 = 1029.740(28) MHz (2σ uncertainty) from RR-RCS transients measured in a pulsed seeded supersonic jet, where essentially only the v = 0 state is populated. Using this B 0 value, RR-RCS measurements in a room temperature gas cell give the rotational constants B v of the five lowest-lying thermally populated vibrationally excited states ν7/8, ν9, ν11/12, ν13, and ν14/15. Their B v constants differ from B 0 by between −1.02 MHz and +2.23 MHz. Combining the B 0 with the results of all-electron coupled-cluster CCSD(T) calculations of Demaison et al. [Mol. Phys.111, 1539 (2013)] and of our own allow to determine the C-C and C-F semi-experimental equilibrium bond lengths r e(C-C) = 1.3866(3) Å and r e(C-F) = 1.3244(4) Å. These agree with the CCSD(T)/wCVQZ r e bond lengths calculated by Demaison et al. within ±0.0005 Å. We also calculate the semi-experimental thermally averaged bond lengths r g(C-C)=1.3907(3) Å and r g(C-F)=1.3250(4) Å. These are at least ten times more accurate than two sets of experimental gas-phase electron diffraction r g bond lengths measured in the 1960s.

Modelling and Validation of a Mass Imbalance Oscillation Generator to Harvest Heart Motion Energy

An autonomous energy source within a human body is of key importance in the development of medical implants. This work deals with the modelling and the validation of an energy harvesting device which converts the myocardial contractions into electrical energy. The mechanism consists of a clockwork from a commercially available wrist watch. We developed a physical model which is able to predict the total amount of energy generated when applying an external excitation. For the validation of the model, a custom-made hexapod robot was used to accelerate the harvesting device along a given trajectory. We applied forward kinematics to determine the actual motion experienced by the harvesting device. The motion provides translational as well as rotational motion information for accurate simulations in three-dimensional space. The physical model could be successfully validated.

Gust wind tunnel study on ballast pick-up by high-speed trains

This paper describes the experimental setup, procedure, and results obtained, concerning the dynamics of a body lying on a floor, attached to a hinge, and exposed to an unsteady flow, which is a model of the initiation of rotational motion of ballast stones due to the wind generated by the passing of a high-speed train. The idea is to obtain experimental data to support the theoretical model developed in Sanz-Andres and Navarro-Medina (J Wind Eng Ind Aerodyn 98, 772–783, (2010), aimed at analyzing the initial phase of the ballast train-induced-wind erosion (BATIWE) phenomenon. The experimental setup is based on an open circuit, closed test section, low-speed wind tunnel, with a new sinusoidal gust generator mechanism concept, designed and built at the IDR/UPM. The tunnel’s main characteristic is the ability to generate a flow with a uniform velocity profile and sinusoidal time fluctuation of the speed. Experimental results and theoretical model predictions are in good agreement.

On the chaotic rotation of a liquid-filled gyrostat via the Melnikov-Holmes-Marsden integral

The non-linear motions of a gyrostat with an axisymmetrical, fluid-filled cavity are investigated. The cavity is considered to be completely filled with an ideal incompressible liquid performing uniform rotational motion. Helmholtz theorem, Euler's angular momentum theorem and Poisson equations are used to develop the disturbed Hamiltonian equations of the motions of the liquid-filled gyrostat subjected to small perturbing moments. The equations are established in terms of a set of canonical variables comprised of Euler angles and the conjugate angular momenta in order to facilitate the application of the Melnikov-Holmes-Marsden (MHM) method to investigate homoclinic/heteroclinic transversal intersections. In such a way, a criterion for the onset of chaotic oscillations is formulated for liquid-filled gyrostats with ellipsoidal and torus-shaped cavities and the results are confirmed via numerical simulations. (c) 2006 Elsevier Ltd. All rights reserved.

Generic decoupled image-based visual servoing for cameras obeying the unified projection model

In this paper a generic decoupled imaged-based control scheme for calibrated cameras obeying the unified projection model is proposed. The proposed decoupled scheme is based on the surface of object projections onto the unit sphere. Such features are invariant to rotational motions. This allows the control of translational motion independently from the rotational motion. Finally, the proposed results are validated with experiments using a classical perspective camera as well as a fisheye camera mounted on a 6 dofs robot platform.

Decoupled image-based visual servoing for cameras obeying the unified projection model

This paper proposes a generic decoupled imagebased control scheme for cameras obeying the unified projection model. The scheme is based on the spherical projection model. Invariants to rotational motion are computed from this projection and used to control the translational degrees of freedom. Importantly we form invariants which decrease the sensitivity of the interaction matrix to object depth variation. Finally, the proposed results are validated with experiments using a classical perspective camera as well as a fisheye camera mounted on a 6-DOF robotic platform.