Analytical and semi-analytical analysis of an artificial satellite's rotational motion

The rotational motion of an artificial satellite is studied by considering torques produced by gravity gradient and direct solar radiation pressure. A satellite of circular cylinder shape is considered here, and Andoyers variables are used to describe the rotational motion. Expressions for direct solar radiation torque are derived. When the earth's shadow is not considered, an analytical solution is obtained using Lagrange's method of variation of parameters. A semi-analytical procedure is proposed to predict the satellite's attitude under the influence of the earth's shadow. The analytical solution shows that angular variables are linear and periodic functions of time while their conjugates suffer only periodic variations. When compared, numerical and analytical solutions have a good agreement during the time range considered.

Study of Stability of Rotational Motion of Spacecraft with Canonical Variables

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Model Coupling Vibrational and Rotational Motion for the DNA Molecule

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

Influence of Earth's shadow on the rotational motion of an artificial satellite perturbed by solar radiation torque

A semi-analytical approach is proposed to study the rotational motion of an artificial satellite under the influence of the torque due to the solar radiation pressure and taking into account the influence of Earth's shadow. The Earth's shadow is introduced in the equations for the rotational motion as a function depending on the longitude of the Sun, on the ecliptic's obliquity and on the orbital parameters of the satellite. By mapping and computing this function, we can get the periods in which the satellite is not illuminated and the torque due to the solar radiation pressure is zero. When the satellite is illuminated, a known analytical solution is used to predict the satellite's attitude. This analytical solution is expressed in terms of Andoyer's variables and depends on the physical and geometrical properties of the satellite and on the direction of the Sun radiation flux. By simulating a hypothetical circular cylindrical type satellite, an example is exhibited and the results agree quite well when compared with a numerical integration. © 1997 COSPAR. Published by Elsevier Science Ltd.

Semi-analytical study of the rotational motion stability of artificial satellites using quaternions

This study at aims performing the stability analysis of the rotational motion to artificial satellites using quaternions to describe the satellite attitude (orientation on the space). In the system of rotational motion equations, which is composed by four kinematic equations of the quaternions and by the three Euler equations in terms of the rotational spin components. The influence of the gravity gradient and the direct solar radiation pressure torques have been considered. Equilibrium points were obtained through numerical simulations using the softwares Matlab and Octave, which are then analyzed by the Routh-Hurwitz Stability Criterion.

FREQUENCY DOMAIN CHARACTERIZATION OF OPTIC FLOW AND VISION-BASED OCELLAR SENSING FOR ROTATIONAL MOTION

The structure of an animal’s eye is determined by the tasks it must perform. While vertebrates rely on their two eyes for all visual functions, insects have evolved a wide range of specialized visual organs to support behaviors such as prey capture, predator evasion, mate pursuit, flight stabilization, and navigation. Compound eyes and ocelli constitute the vision forming and sensing mechanisms of some flying insects. They provide signals useful for flight stabilization and navigation. In contrast to the well-studied compound eye, the ocelli, seen as the second visual system, sense fast luminance changes and allows for fast visual processing. Using a luminance-based sensor that mimics the insect ocelli and a camera-based motion detection system, a frequency-domain characterization of an ocellar sensor and optic flow (due to rotational motion) are analyzed. Inspired by the insect neurons that make use of signals from both vision sensing mechanisms, advantages, disadvantages and complementary properties of ocellar and optic flow estimates are discussed.

Measurement of the rotational inertia of bodies by using mechanical spectroscopy

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

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.

Tilted boxes on inclined planes

We propose the study of a box placed on an inclined plane, with an initial tilt with respect to the plane. This is a paradigmatic example of the role played by friction as a link between translational and rotational motion. This example has two advantages over the usual example of a sphere (or cylinder) rolling down an inclined plane. First, it provides a good model for a much greater variety of "real-life" situations. Second, it exhibits a much richer structure in parameter space, even when the box starts from rest. (C) 2000 American Association of Physics Teachers.

Vector of coordinates, velocities and accelerations

This chapter describes the how the vector of coordinates are defined in the formulation of spatial multibody systems. For this purpose, the translational motion is described in terms of Cartesian coordinates, while rotational motion is specified using the technique of Euler parameters. This approach avoids the computational difficulties associated with the singularities in the case of using Euler angles or Bryant angles. Moreover, the formulation of the velocities vector and accelerations vector is presented and analyzed here. These two sets of vectors are defined in terms of translational and rotational coordinates.

Cardiac rotation and relaxation after anterolateral myocardial infarction.

BACKGROUND: Both systolic and diastolic dysfunction have been observed in patients with anterolateral myocardial infarction. Diastolic dysfunction is related to disturbances in relaxation and diastolic filling. OBJECTIVE: To analyse cardiac rotation, regional shortening and diastolic relaxation in patients with anterolateral infarction. METHODS: Cardiac rotation and relaxation in controls and patients with chronic anterolateral infarction were assessed by myocardial tagging. Myocardial tagging is based on magnetic resonance imaging and allows us to label specific myocardial regions for imaging cardiac motion (rotation, translation and radial displacement). A rectangular grid was placed on the myocardium (basal, equatorial and apical short-axis plane) of each of 18 patients with chronic anterolateral infarction and 13 controls. Cardiac rotation, change in area and shortening of circumference were determined in each case. RESULTS: The left ventricle in controls performs a systolic wringing motion with a clockwise rotation at the base and a counterclockwise rotation at the apex when viewed from the apex. During relaxation a rotational motion in the opposite direction (namely untwisting) can be observed. In patients with anterolateral infarction, there is less systolic rotation at the apex and diastolic untwisting is delayed and prolonged in comparison with controls. In the presence of a left ventricular aneurysm (n = 4) apical rotation is completely lost. There is less shortening of circumference in infarcted and remote regions. CONCLUSIONS: The wringing motion of the myocardium might be an important mechanism involved in maintaining normal cardiac function with minimal expenditure of energy. This mechanism no longer operates in patients with left ventricular aneurysms and operates significantly less than normal in those with anterolateral hypokinaesia. Diastolic untwisting is significantly delayed and prolonged in patients with anterolateral infarction, which could explain the occurrence of diastolic dysfunction in these patients.

Mechanical properties of cultured human airway smooth muscle cells from 0.05 to 0.4 Hz.

We investigated the rheological properties of living human airway smooth muscle cells in culture and monitored the changes in rheological properties induced by exogenous stimuli. We oscillated small magnetic microbeads bound specifically to integrin receptors and computed the storage modulus (G') and loss modulus (G") from the applied torque and the resulting rotational motion of the beads as determined from their remanent magnetic field. Under baseline conditions, G' increased weakly with frequency, whereas G" was independent of the frequency. The cell was predominantly elastic, with the ratio of G" to G' (defined as eta) being ~0.35 at all frequencies. G' and G" increased together after contractile activation and decreased together after deactivation, whereas eta remained unaltered in each case. Thus elastic and dissipative stresses were coupled during changes in contractile activation. G' and G" decreased with disruption of the actin fibers by cytochalasin D, but eta increased. These results imply that the mechanisms for frictional energy loss and elastic energy storage in the living cell are coupled and reside within the cytoskeleton.

Cardiac rotation and relaxation in patients with aortic valve stenosis.

BACKGROUND: Diastolic dysfunction with delayed relaxation and abnormal passive elastic properties has been described in patients with severe pressure overload hypertrophy. The purpose of this study was to evaluate the time course of rotational motion of the left ventricle in patients with aortic valve stenosis using myocardial tagging. METHODS: Myocardial tagging is a non-invasive method based on magnetic resonance which makes it possible to label ('tag') specific myocardial regions. From the motion of the tag's cardiac rotation, radial displacement and translational motion can be determined. In 12 controls and 13 patients with severe aortic valve stenosis systolic and diastolic wall motion was assessed in an apical and basal short axis plane. RESULTS: The normal left ventricle performs a systolic wringing motion around the ventricular long axis with clockwise rotation at the base (-4.4+/-1.6 degrees) and counter-clockwise rotation at the apex (+6.8+/-2.5 degrees) when viewed from the apex. During early diastole an untwisting motion can be observed which precedes diastolic filling. In patients with aortic valve stenosis systolic rotation is reduced at the base (-2.4+/-2.0 degrees; P<0.01) but increased at the apex (+12.0+/-6.0 degrees; P<0.05). Diastolic untwisting is delayed and prolonged with a decrease in normalized rotation velocity (-6.9+/-1.1 s(-1)) when compared to controls (-10.7+/-2.2 s(-1); P<0.001). Maximal systolic torsion is 8.0+/-2.1 degrees in controls and 14.1+/-6.4 degrees (P<0.01) in patients with aortic valve stenosis. CONCLUSIONS: Left ventricular pressure overload hypertrophy is associated with a reduction in basal and an increase in apical rotation resulting in increased torsion of the ventricle. Diastolic untwisting is delayed and prolonged. This may explain the occurrence of diastolic dysfunction in patients with severe pressure overload hypertrophy.

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.