We consider the problem of finding the generalized potential function V = Ui(q1, q2,..., qn)qi + U(q1, q2,...;qn) compatible with prescribed dynamical trajectories of a holonomic system. We obtain conditions necessary for the existence of solutions to the problem: these can be cast into a system of n – 1 first order nonlinear partial differential equations in the unknown functions U1, U2,...;, Un, U. In particular we study dynamical systems with two degrees of freedom. Using adapted coordinates on the configuration manifold M2 we obtain, for potential function U(q1, q2), a classic first kind of Abel ordinary differential equation. Moreover, we show that, in special cases of dynamical interest, such an equation can be solved by quadrature. In particular we establish, for ordinary potential functions, a classical formula obtained in different way by Joukowsky for a particle moving on a surface.Work performed with the support of the Gruppo Nazionale di Fisica Matematica (G.N.F.M.) of the Italian National Research Council. 相似文献
Investigation of deposits for traditional extraction activities (metals and coal) has generally been based on determining grade, or content, of the required material. In order to apply the grade concept to an ornamental rock such as slate, it is first necessary to define the variables that determine both the geotechnical recovery rate for the rock mass — which conditions the size of the extracted blocks – and the aesthetic features of the slate — which define the quality of the slabs as potential roofing material.
For this research, geotechnical and aesthetic data for a slate deposit were collected from 16 continuous core borehole samples. A fuzzy expert system was then developed using this data, defining the rock mass recovery rate and slab quality in accordance with the criteria of a slate expert, producing as a final output a zonation of the deposit in terms of top quality slate, medium quality slate or waste.
A mathematical model based on fuzzy logic was chosen due to the fact that the boundaries between different quality groups in a deposit are not clearly distinguished. Moreover, quality also depends on a company's infrastructures for transformation of the blocks, and also on its commercial strategies. 相似文献
A study has been done for analysing soil nailed cuts with circular type wedge failure by friction circle method. Various parameters
such as nail length, nail diameter, nail inclination, wall inclination and angle of internal friction of soil have been considered
to determine the factor of safety of nailed open cuts. The study shows that for cohesionless soil nailed cut, factor of safety
increase with increase of parameters like angle of internal friction of soil, length of nail (L) versus height of cut (H) ratio, cohesion of soil and nail inclination (upto 15°) with horizontal. The study revealed that nails grouted with cement
perform better than driven nails. A case study further confirms the analytical findings.
Received 7 October 相似文献