A comprehensive dynamic model for class-1 tensegrity systems based on quaternions

In this paper we propose a new dynamic model, based on quaternions, for tensegrity systems of class-1. Quaternions are used to represent orientations of a rigid body in the 3-dimensional space eliminating the problem of singularities. Moreover, the equations based on quaternions allow to perform more precise calculations and simulations because they do not use trigonometric functions for the representation of angles. We present a thorough introduction of tensegrities and the current state of research. We also introduce the quaternions and provide in the appendix some important details and useful properties. Applying the Euler–Lagrange approach we derive a comprehensive dynamic model, first for a simple rigid bar in the space and, at last, for a class-1 tensegrity system. We present two model forms: a matrix and a vectorial form. The first more compact and easier to write, the latter more suitable to apply the tools and the theory based on vector fields.     

Hyperelliptic parametrizations of $$\pmb {\mathbb {Q}}$$ Q -curves

The Ramanujan Journal - In this paper, our aim is to find the radii of starlikeness and convexity of the Ramanujan type function for three different kinds of normalization by using their...     

Parallel Newton Two-Stage Multisplitting Iterative Methods for Nonlinear Systems

Parallel Newton two-stage iterative methods to solve nonlinear systems are studied. These algorithms are based on both the multisplitting technique and the two-stage iterative methods. Convergence properties of these methods are studied when the Jacobian matrix is either monotone or an H-matrix. Furthermore, in order to illustrate the performance of the algorithms studied, computational results about these methods on a distributed memory multiprocessor are discussed.This revised version was published online in October 2005 with corrections to the Cover Date.     

Improved thermosets obtained from cycloaliphatic epoxy resins and γ‐butyrolactone with lanthanide triflates as initiators. I. Study of curing by differential scanning calorimetry and Fourier transform infrared

3,4‐Epoxycyclohexylmethyl 3,4‐epoxycyclohexane carboxylate was cured with different proportions of γ‐butyrolactone with lanthanum, samarium, and ytterbium triflates as catalysts. The curing was studied with differential scanning calorimetry (DSC) and Fourier transform infrared in the attenuated‐total‐reflection mode (FTIR/ATR). FTIR/ATR was used to monitor the competitive reactive processes and to quantify the evolution of the epoxide, lactone, and intermediate spiroorthoester groups. The glass‐transition temperature of the crosslinked materials was high and increased when the proportion of lactone decreased. The kinetics were studied with DSC experiments and were analyzed with isoconversional procedures. The differences in the reactivities of the systems were related to the Lewis acidity of the lanthanide salt used as the initiator. An increase in the proportion of lactone produced an increase in the reaction rate. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2337‐2347, 2005     

An efficient catalytic system for cyclocarbonylation of terpenes into lactones

Three different kinds of representative monoterpenic alcohol are involved in the palladium‐catalysed cyclocarbonylation reaction. Lactone formation is shown to occur when cyclic ( 1 ), tertiary ( 3 ) and primary allylic alcohol ( 7 ) functions are reacted, in the presence of CO with [HPd(SnCl₃)L₂] as the active catalytic species. Good yields and selectivities can easily be reached for isopulegol ( 1 ), and dihydromyrcenol ( 3 ). However, more modest results are obtained for the functionalization of geraniol into the original lactone ( 9 ). This lactone can be largely favoured by using a basic chelating diphosphine ligand such as 1,4‐bis(diphenylphosphino)butane. Copyright © 2005 John Wiley & Sons, Ltd.     

Reduction of the shrinkage of thermosets by the cationic curing of mixtures of diglycidyl ether of bisphenol A and 6,6‐dimethyl‐(4,8‐dioxaspiro[2.5]octane‐5,7‐dione)

Ytterbium and lanthanum triflates were used as initiators to cure mixtures of diglycidyl ether of bisphenol A and 6,6‐dimethyl‐(4,8‐dioxaspiro[2.5]octane‐5,7‐dione) in several proportions. The evolution of the epoxy and 6,6‐dimethyl‐(4,8‐dioxaspiro[2.5]octane‐5,7‐dione) bands during curing and the linear ester groups in the final materials were evaluated with Fourier transform infrared in the attenuated‐total‐reflection mode. The use of a conventional cationic initiator, boron trifluoride monoethylamine, was also studied to test the advantages of lanthanide triflates. The shrinkage after curing and the thermal degradability of the materials with variations in the comonomer ratio and the initiator were evaluated and related to the chemical structure of the final network. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6869–6879, 2006     

Cationic copolymerization of cycloaliphatic epoxy resin with a spirobislactone with lanthanum triflate as initiator: I. Characterization and shrinkage

3,4‐Epoxycyclohexylmethyl 3,4‐epoxycyclohexane carboxylate (ECH) was cured with different proportions of 1,6‐dioxaspiro [4,4]nonane‐2,7‐dione (s(γ‐BL)) using lanthanum triflate as a catalyst. The shrinkage undergone during curing was monitored by means of thermomechanical analysis (TMA) in isothermal experiments. Fourier transform infrared spectroscopy in attenuated‐total‐reflection mode (FTIR/ATR) was used to study the evolution of lactone, epoxide, and intermediate spiroorthoester (SOE) groups to identify the different reactions that take place during the curing process. DSC was used to study the thermal characteristics of the curing process and to assess the glass‐transition temperature (T_g) of the cured material. The dynamic mechanical properties of the cured material were determined based on the data obtained by DMTA. An increase in the proportion of s(γ‐BL) led to a decrease in the gelation time and the shrinkage after gelation. By combining the data obtained by TMA and FTIR/ATR, it was also possible to identify the reactive processes responsible for the shrinkage. It was observed that an increase in the proportion of s(γ‐BL) also increases the speed of the curing process and modifies the structure of the material, thus giving rise to more flexible materials. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3421–3432, 2005