Canonical transformations for space trajectory optimization

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76506/1/AIAA-1992-4509-414.pd

Minimum-fuel, power-limited transfers between coplanar elliptical orbits

Two methods of computing coplanar, minimum-fuel, power-limited transfers are developed, based on approximate solutions obtained by the averaging method. In the first method, the average solution provides estimates of the initial adjoint variables; in the second, it provides approximations of the optimal controls in feedback form. Both trajectory variables and orbit elements are used in developing these methods. Canonical transformations are derived to convert between these sets of coordinates. The accuracy of the methods for computing coplanar, minimum-fuel, power-limited transfers is assessed for a variety of initial and final orbits. Some initial steps are taken toward the characterization of coplanar, minimum-fuel, power-limited transfers for a wide range of thrust to weight ratios. Circle to ellipse and ellipse to ellipse transfers are considered. Details of the trajectories and thrust profiles for a few illustrative cases are presented. These trajectories and thrust profiles are compared to analytical results obtained using the averaging method and to the analytic solution for infinitesimal transfer. The secular behavior of minimum-fuel transfer is predicted by the averaging results. The shape and orientation of the osculating orbits are predicted quantitatively, while the size is predicted qualitatively. The analytic solution for infinitesimal transfer predicts the qualitative behavior of the thrust during each revolution. Some general principles of minimum-fuel, power-limited transfer are revealed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31013/1/0000688.pd

Evaluation of a High Throughput Starch Analysis Optimised for Wood

Starch is the most important long-term reserve in trees, and the analysis of starch is therefore useful source of physiological information. Currently published protocols for wood starch analysis impose several limitations, such as long procedures and a neutralization step. The high-throughput standard protocols for starch analysis in food and feed represent a valuable alternative. However, they have not been optimised or tested with woody samples. These have particular chemical and structural characteristics, including the presence of interfering secondary metabolites, low reactivity of starch, and low starch content. In this study, a standard method for starch analysis used for food and feed (AOAC standard method 996.11) was optimised to improve precision and accuracy for the analysis of starch in wood. Key modifications were introduced in the digestion conditions and in the glucose assay. The optimised protocol was then evaluated through 430 starch analyses of standards at known starch content, matrix polysaccharides, and wood collected from three organs (roots, twigs, mature wood) of four species (coniferous and flowering plants). The optimised protocol proved to be remarkably precise and accurate (3%), suitable for a high throughput routine analysis (35 samples a day) of specimens with a starch content between 40 mg and 21 µg. Samples may include lignified organs of coniferous and flowering plants and non-lignified organs, such as leaves, fruits and rhizomes