Dynamic Instabilities in Slender Space Launch Vehicles under Propulsive Thrust and Aerodynamic Forces

A mechanics based linear analysis of the problem of dynamic instabilities in slender space launch vehicles is undertaken. The flexible body dynamics of the moving vehicle is studied in an inertial frame of reference, including velocity induced curvature effects, which have not been considered so far in the published literature. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic forces and the propulsive thrust of the vehicle. The effects of the coupling between the combustion process (mass variation, developed thrust etc.) and the variables involved in the flexible body dynamics (displacements and velocities) are clearly brought out. The model is one-dimensional, and it can be employed to idealised slender vehicles with complex shapes. Computer simulations are carried out using a standard eigenvalue problem within h-p finite element modelling framework. Stability regimes for a vehicle subjected to propulsive thrust are validated by comparing the results from published literature. Numerical simulations are carried out for a representative vehicle to determine the instability regimes with vehicle speed and propulsive thrust as the parameters. The phenomena of static instability (divergence) and dynamic instability (flutter) are observed. The results at low Mach number match closely with the results obtained from previous models published in the literature.

Hybrid Simulation of Queuing-System Dynamics

This paper presents a simple hybrid computer technique to study the transient behaviour of queueing systems. This method is superior to stand-alone analog or digital solution because the hardware requirement is excessive for analog technique whereas computation time is appreciable in the latter case. By using a hybrid computer one can share the analog hardware thus requiring fewer integrators. The digital processor can store the values, play them back at required time instants and change the coefficients of differential equations. By speeding up the integration on the analog computer it is feasible to solve a large number of these equations very fast. Hybrid simulation is even superior to the analytic technique because in the latter case it is difficult to solve time-varying differential equations.

Symmetries and constraints in generalized Hamiltonian dynamics

A general analysis of symmetries and constraints for singular Lagrangian systems is given. It is shown that symmetry transformations can be expressed as canonical transformations in phase space, even for such systems. The relation of symmetries to generators, constraints, commutators, and Dirac brackets is clarified.

Dynamics of a class of social interaction systems

A mathematical model of social interaction in the form of two coupler! first-order non-linear differential equations, forms the topic of this study. This non-conservative model io representative of such varied social interaction problems as coexisting sub-populations of two different species, arms race between two rival countries and the like. Differential transformation techniques developed elsewhere in the literature are seen to be effective tools of dynamic analysis of this non-linear non-conservative mode! of social interaction process.

Dynamics of carbohydrateâlectin interaction The interaction p-nitrophenyl-β-D-galactose with a lectin from Ricinius communis

L&in-induced agglutination is a complex process determined by several factprs such as the nature of lectin (valency, binding constant) the properties of cell membrane (fluidity, distribution of lectin receptor sites) and the metabolic state of the cell (microvilli, microtubules, microfilament) [l-3].

Dynamics of Circulating Concentrations of Gonadotropins and Ovarian Hormones Throughout the Menstrual Cycle in the Bonnet Monkey: Role of Inhibin A in the Regulation of Follicle-Stimulating Hormone Secretion

In higher primates, increased circulating follicle-stimulating hormone (FSH) levels seen during late menstrual cycle and during menstruation has been suggested to be necessary for initiation of follicular growth, recruitment of follicles and eventually culminating in ovulation of a single follicle. With a view to establish the dynamics of circulating FSH secretion with that of inhibin A (INH A) and progesterone (P-4)secretions during the menstrual cycle, blood was collected daily from bonnet monkeys beginning day 1 of the menstrual cycle up to 35 days. Serum INH A levels were low during early follicular phase, increased significantly coinciding with the mid cycle luteinizing hormone (LH) surge to reach maximal levels during the mid luteal phase before declining at the late luteal phase, essentially paralleling the pattern Of P-4 secretion seen throughout the luteal phase. Circulating FSH levels were low during early and mid luteal phases, but progressively increased during the late luteal phase and remained high for few days after the onset of menses. In another experiment, lutectomy performed during the mid luteal phase resulted in significant decrease in INH A concentration within 2 hr (58.3 +/- 2 vs. 27.3 +/- 3 pg/mL), and a 2- to 3-fold rise in circulating FSH levels by 24 hr (0.20 +/- 0.02 vs. 0.53 +/- 0.14 ng/mL) that remained high until 48 hr postlutectomy. Systemic administration of Cetrorelix (150 mu g/kg body weight), a gonadotropin releasing hormone receptor antagonist, at mid luteal phase in monkeys led to suppression of serum INH A and P-4 concentrations 24 hr post treatment, but circulating FSH levels did not change. Administration of exogenous LH, but not FSH, significantly increased INH A concentration. The results taken together suggest a tight coupling between LH and INH A secretion and that INH A is largely responsible for maintenance of low FSH concentration seen during the luteal phase. Am. J. Primatol. 71:817-824, 2009.

A Modified Dubins Method for Optimal Path Planning of a Miniature Air Vehicle Converging to a Straight Line Path

This paper presents a Dubins model based strategy to determine the optimal path of a Miniature Air Vehicle (MAV), constrained by a bounded turning rate, that would enable it to fly along a given straight line, starting from an arbitrary initial position and orientation. The method is then extended to meet the same objective in the presence of wind which has a magnitude comparable to the speed of the MAV. We use a modification of the Dubins' path method to obtain the complete optimal solution to this problem in all its generality.

Modified ILMI algorithm for practical PID/PD implementation on a Micro Air Vehicle

This paper extends the iterative linear matrix inequality algorithm (ILMI) for systems having non-ideal PI, PD and PID implementations. The new algorithm uses the practical implementation of the feedback blocksto form the equivalent static output feedback plant. The LMI based synthesis techniques are used in the algorithm to design a multi-loop, multi-objective fixed structure control. The benefits of such a control design technique are brought out by applying it to the lateral stabilizing and tracking feedback control problem of a 30cm wingspan micro air vehicle.

Determination of optimal trajectory under design constraints for a satellite launch vehicle

An optimal pitch steering programme of a solid-fuel satellite launch vehicle to maximize either (1) the injection velocity at a given altitude, or (2) the size of circular orbit, for a given payload is presented. The two-dimensional model includes the rotation of atmosphere with the Earth, the vehicle's lift and drag, variation of thrust with time and altitude, inverse-square gravitational field, and the specified initial vertical take-off. The inequality constraints on the aerodynamic load, control force, and turning rates are also imposed. Using the properties of the central force motion the terminal constraint conditions at coast apogee are transferred to the penultimate stage burnout. Such a transformation converts a time-free problem into a time-fixed one, reduces the number of terminal constraints, improves accuracy, besides demanding less computer memory and time. The adjoint equations are developed in a compact matrix form. The problem is solved on an IBM 360/44 computer using a steepest ascent algorithm. An illustrative analysis of a typical launch vehicle establishes the speed of convergence, and accuracy and applicability of the algorithm.

Effects of solar radiation pressure and Aerodynamic forces on satelliteattitude Dynamics and their utilization for Control: a survey

The environmcnl exerts an important inJuence on the pefirmance of space systems. A brief rel'iew of mo.s/ of the studies, pre.~ented over the past eightem years, relating to the influence ar7d the possible utilization of thc solar radiation pressure &d aero&namic forces, with particular reference to attitude dynamics and control qf satellites is presented here. The semi-passive stabilizers employing rhese forces show p~qmise of long life, low power and economic sjsfems, which though slower in response, compare we1I wit11 the octiw coi~trollers. It is felt that mud more attention is necessary to the actual implema~tution of these ideas and devices: some of which me quite ingenious und unique.

Dissipative dynamics of a harmonic oscillator: A nonperturbative approach

Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of noninteracting oscillators. We follow a nonperturbative approach, proposed earlier by us for the free Brownian particle. The diffusion constants are calculated analytically and the positivity of the master equation is shown to hold above a critical temperature. We compare the long time behavior of the average kinetic and potential energies with known thermodynamic results. In the limit of vanishing oscillator frequency of the system, we recover the results of the free Brownian particle.

Entanglement production due to quench dynamics of an anisotropic XY chain in a transverse field

We compute concurrence and negativity as measures of two-spin entanglement generated by a power-law quench (characterized by a rate tau(-1) and an exponent alpha) which takes an anisotropic XY chain in a transverse field through a quantum critical point (QCP). We show that only spins separated by an even number of lattice spacings get entangled in such a process. Moreover, there is a critical rate of quench, tau(-1)(c), above which no two-spin entanglement is generated; the entire entanglement is multipartite. The ratio of the entanglements between consecutive even neighbors can be tuned by changing the quench rate. We also show that for large tau, the concurrence (negativity) scales as root alpha/tau(alpha/tau), and we relate this scaling behavior to defect production by the quench through a QCP.

Coarse-Grained Molecular Dynamics Simulation of the Aggregation Properties of Multiheaded Cationic Surfactants in Water

The aggregation property of multiheaded surfactants has been investigated by constant pressure molecular dynamics (MD) simulation in aqueous medium. The model multiheaded surfactants contain more than one headgroup (x = 2, 3, and 4) for a single tail group. This increases the hydrophilic charge progressively over the hydrophobic tail which has dramatic consequences in the aggregation behavior. In particular, we have looked at the change in the aggregation property such as critical micellar concentration (cmc), aggregation number, and size of the micelles for the multiheaded surfactants in water. We find with increasing number of headgroups of the Multiheaded surfactants that the cmc values increase and the aggregation numbers as well as the size of the micelles decrease. These trends are in agreement with the experimental findings as reported earlier with x = 1, 2, and 3. We also predict the aggregation properties of multiheaded surfactant With four headgroups (x = 4) for which no experimental studies exist yet.

Synthesis, characterization, thermal degradation, and comparative chain dynamics studies of weak-link polysulfide polymers

Synthesis, spectroscopic and thermal characterization of two new classes of polysulfide polymers: poly[1(phenoxymethyl) ethylene polysulfide] (PPMEP), and poly [1-(phenoxy) ethylene polysulfide] (PPEP) is presented. The direct pyrolysis mass spectrometry (DP-MS) technique, used to study the thermal degradation behavior of these polysulfide polymers, indicated that the polymers underwent degradation through the weak-links scission. The thermal stability of the polysulfide polymers decreased as the ``rank'' (number of sulfur atoms in the polysulfide linkage; n=1, 2, 4) increased. The main-chain flexibility of these polysulfide polymers in terms of their C-13 NMR spinlattice relaxation time (T-1) measurements on the backbone methine (-CH-) and methylene (-CH2-) carbons are reported here for the first time. A comparative study of the solution chain dynamics indicated that it increased as ``rank'' of the polysulfide linkages decreased as well as by introducing side chain spacers such as, ether (-O-) or methyleneoxy (-CH2O-) groups.

Ab initio molecular dynamics simulations of excited hydrogen halides and methyl halides

Using excited-state ab initio molecular dynamics simulations employing the complete-active-space self-consistent-field approach, we study the mechanism of photodissociation in terms of time evolution of structure, kinetic energy, charges and potential energy for the first excited state of hydrogen halides and methyl halides. Although the hydrogen halides and methyl halides are similar in the photodissociation mechanism, their dynamics are slightly different. The presence of the methyl group causes delay in photodissociation as compared to hydrogen halides.