Stability condition for vertical oscillation of 3-dim heavy spring elastic pendulum

2008 ◽  
Vol 13 (3) ◽  
pp. 155-165 ◽  
Author(s):  
P. Pokorny
2021 ◽  
Vol 103 (3) ◽  
pp. 2841-2853
Author(s):  
Anurag ◽  
Basudeb Mondal ◽  
Tirth Shah ◽  
Sagar Chakraborty
Keyword(s):  

Author(s):  
Madoka Muroishi ◽  
Akira Yakita

AbstractUsing a small, open, two-region economy model populated by two-period-lived overlapping generations, we analyze long-term agglomeration economy and congestion diseconomy effects of young worker concentration on migration and the overall fertility rate. When the migration-stability condition is satisfied, the distribution of young workers between regions is obtainable in each period for a predetermined population size. Results show that migration stability does not guarantee dynamic stability of the economy. The stationary population size stability depends on the model parameters and the initial population size. On a stable trajectory converging to the stationary equilibrium, the overall fertility rate might change non-monotonically with the population size of the economy because of interregional migration. In each period, interregional migration mitigates regional population changes caused by fertility differences on the stable path. Results show that the inter-regional migration-stability condition does not guarantee stability of the population dynamics of the economy.


2020 ◽  
Vol 6 (1) ◽  
pp. e000963
Author(s):  
Sheeba Davis ◽  
Aaron Fox ◽  
Jason Bonacci ◽  
Fiddy Davis

Grounded running predominantly differs from traditional aerial running by having alternating single and double stance with no flight phase. Approximately, 16% of runners in an open marathon and 33% of recreational runners in a 5 km running event adopted a grounded running technique. Grounded running typically occurs at a speed range of 2–3 m·s−1, is characterised by a larger duty factor, reduced vertical leg stiffness, lower vertical oscillation of the centre of mass (COM) and greater impact attenuation than aerial running. Grounded running typically induces an acute increase in metabolic cost, likely due to the larger duty factor. The increased duty factor may translate to a more stable locomotion. The reduced vertical oscillation of COM, attenuated impact shock, and potential for improved postural stability may make grounded running a preferred form of physical exercise in people new to running or with low loading capacities (eg, novice overweight/obese, elderly runners, rehabilitating athletes). Grounded running as a less impactful, but metabolically more challenging form, could benefit these runners to optimise their cardio-metabolic health, while at the same time minimise running-related injury risk. This review discusses the mechanical demands and energetics of grounded running along with recommendations and suggestions to implement this technique in practice.


Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1447
Author(s):  
Jose P. Suárez ◽  
Agustín Trujillo ◽  
Tania Moreno

Showing whether the longest-edge (LE) bisection of tetrahedra meshes degenerates the stability condition or not is still an open problem. Some reasons, in part, are due to the cost for achieving the computation of similarity classes of millions of tetrahedra. We prove the existence of tetrahedra where the LE bisection introduces, at most, 37 similarity classes. This family of new tetrahedra was roughly pointed out by Adler in 1983. However, as far as we know, there has been no evidence confirming its existence. We also introduce a new data structure and algorithm for computing the number of similarity tetrahedral classes based on integer arithmetic, storing only the square of edges. The algorithm lets us perform compact and efficient high-level similarity class computations with a cost that is only dependent on the number of similarity classes.


2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
H. Saberi Najafi ◽  
A. Refahi Sheikhani ◽  
A. Ansari

We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure.


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