A Variational Derivation of Equations of Motion With Contact Constraints Using SE(3)

For rigid-body systems subjected to non-holonomic constraints, a streamlined method is presented to derive a minimum number of analytical equations of motion. To illustrate the method, a rolling disk problem is considered. In kinematics, an orthonormal coordinate system is attached to the center of mass together with additional coordinate systems introduced to define the connection path. For each coordinate system, a moving frame is defined by explicitly writing the coordinate vector basis and the position vector of the origin, whereby the attitude of the coordinate vector basis and the coordinates of the origin are compactly stored in a 4 × 4 frame connection matrix of the special Euclidean group, SE(3). Contact velocity constraints are transformed to pfaffians to obtain the associated variational constraints. In kinetics, the principle of virtual work is employed. The desired equations of motion are obtained by expressing the translational and angular velocities at the center of mass as the linear functions of the generalized velocities with the coefficients stored in [B]-matrix, and reducing it to [B*]-matrix after incorporating the contact constraints. The method can be easily extended to multi-body systems with both holonomic and non-holonomic constraints.

Assessment of Hazardous Exogenous Processes of the Mondy Depression Based on Morphometric and Landscape Analysis

The authors consider the application of geoinformation mapping in the analysis of hazardous processes using space images, digital terrain models, as well as comparative analysis of the landscape map and the map of hazardous exogenous processes. As a result, a large-scale map of hazardous processes within the Mondy depression was created. At the first stage, space images, physical and geographical conditions were analyzed, as well as the morphometric indicators of the territory. On the basis of that analysis classes of hazardous exogenous processes that affected the landscapes of the depression were identified. Further the classes of hazardous exogenous processes were compared with landscape facies, within the contours of which hazardous processes of different intensity are common. Calculation of hazardous exogenous processes using the data of morphometric indicators was made, the information on the long-term change in the main elements of the climate of the study area obtained. The method of spatial analysis in geographic information systems on a vector basis marked the main hazardous exogenous processes that have developed in the territory of the Mondy depression. The gravitational-slope class, represented by collapses and screes, is most widespread in the investigated area. Fluvial class of the dangerous exogenous processes is mostly indicated by mudflows in the valleys of small and temporary watercourses. Cryogenic class of these processes is least developed.