Structural evolution of the Lesser Himalayan fold-thrust belt of west central Nepal

The Lesser Himalayan fold-thrust belt on the south flank of the Jajarkot klippe in west central Nepal was mapped in detail between the Main Central thrust in the north and the Main Boundary thrust in the south. South of the Jajarkot klippe, the fold-thrust belt involves sandstone, shale and carbonate rocks that are unmetamorphosed in the foreland and increase in metamorphic grade with higher structural position to sub-greenschist facies towards the hinterland. The exposed stratigraphy is correlative with the Proterozoic Ranimata, Sangram, Galyang, Syangia Formations and Lakharpata Group of Western Nepal and overlain by the Paleozoic Tansen and Kali Gandaki Groups. Based on field mapping and cross-section construction, three distinct thrust sheets were identified separated by top-to-the-south thrust faults. From the foreland (south) to the hinterland (north), the first thrust sheet in the immediate hanging wall of the Main Boundary thrust defines an open syncline. The second thrust sheet contains a very broad synformal duplex, which is structurally stacked against the third thrust sheet containing a homoclinal panel of the oldest exposed Proterozoic stratigraphy. Outcrop scale folds throughout the study area are predominantly south vergent, open, and asymmetric reflecting the larger regional scale folding style, which corroborate the top-to-the-south deformation style seen in the faults of the region. Field techniques were complemented with microstructural and quartz crystallographic c-axis preferred orientation analyses using a petrographic microscope and a fabric analyzer, respectively. Microstructural analysis identified abundant strain-induced recrystallization textures and occasional occurrences of top-to-the-south shear-sense indicators primarily in the hinterland rocks in the immediate footwall of the Main Central Thrust. Top-to-the-south shearing is also supported by quartz crystallographic c-axis preferred orientations. Quartz recrystallization textures indicate an increase in deformation temperature towards the Main Central thrust. A line balance estimate indicates that approximately 15 km of crustal shortening was accommodated by folding and faulting in the fold-thrust belt south of the Jajarkot klippe. Additionally, estimations of shortening velocity suggest that the shortening velocity operating in this section of the fold-thrust belt between 23 to 14 Ma was slower than what is currently observed as a result of the ongoing deformation of the Sub-Himalayan fold-thrust belt.

Degeneracy of velocity constraints in rigid body systems

The equations governing the dynamics of rigid body systems with velocity constraints are singular at degenerate configurations in the constraint distribution. In this report, we describe the causes of singularities in the constraint distribution of interconnected rigid body systems with smooth configuration manifolds. A convention of defining primary velocity constraints in terms of orthogonal complements of one-dimensional subspaces is introduced. Using this convention, linear maps are defined and used to describe the space of allowable velocities of a rigid body. Through the definition of these maps, we present a condition for non-degeneracy of velocity constraints in terms of the one dimensional subspaces defining the primary velocity constraints. A method for defining the constraint subspace and distribution in terms of linear maps is presented. Using these maps, the constraint distribution is shown to be singular at configuration where there is an increase in its dimension.