Skinner-Rusk approach to time-dependent mechanics

The geometric approach to autonomous classical mechanical systems in terms of a canonical first-order system on the Whitney sum of the tangent and cotangent bundle, developed by R. Skinner and R. Rusk, is extended to the time-dependent framework

Light-related variation in sapling architecture of three shade-tolerant tree species of the Mexican rain forest

The crown architecture of three shade-tolerant tree species (two subcanopy and one mid-canopy) was analyzed in relation to the light regime of the forest understorey. The aim was to examine to which extent shade-tolerant species variate in their crown architecture. Tree saplings (265) between 50 and 300 cm height, and distributed from understorey to variously-sized canopy gaps, were measured for 13 architectural traits in the lowland rain forest of Los Tuxtlas, Mexico. The analysis showed that the three species changed their architecture as light increased but in a different way. No species conformed to the typical wide-crown type expected for shade-tolerant species, and in contrast they presented some traits of light demanding species. The two sub-canopy species tended to adopt a crown form between a narrow- and wide-crown type, and the mid-canopy species showed more traits of a narrow-crown type. The horizontal crown area appeared as the more related trait to the light and sapling height. It is concluded that despite being shade-tolerant, the Studied species make use of better-lit environments in the forest understorey. The crown architecture of shade-tolerant species is not Lis rigid Lis originally conceived