2011
DOI: 10.1137/100814470
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Abstract: The interpretation of joint kinematics data in terms of displacements is a product of the type of movement, the measurement technique, and the underlying model of the joint implemented in optimization procedures. Kinematic constraints reducing the number of degrees of freedom are expected to compensate for measurement errors and noise, thus, increasing the reproducibility of joint angles. One approach already successfully applied by several groups approximates the healthy human knee joint as a compound hinge j… Show more

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Cited by 54 publications
(72 citation statements)
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“…Since then the method has been applied to many problems. For example, it has been successfully applied in biochemistry [22,27] and to study canards in R 3 [26,39]. Note that the term blow up is also used in other areas of mathematics and can have different meanings, depending on the context.…”
mentioning
confidence: 99%
“…Since then the method has been applied to many problems. For example, it has been successfully applied in biochemistry [22,27] and to study canards in R 3 [26,39]. Note that the term blow up is also used in other areas of mathematics and can have different meanings, depending on the context.…”
mentioning
confidence: 99%
“…From the implicit function theorem, it follows that there exists a unique root z = h(x) of the algebraic equation g(x,z, 1) = 0. Then, the corresponding slow dynamics are given as (17). On the other hand from (12) it is evident that the "blown up" layer equation is (18), wherex is treated as a fixed parameter.…”
Section: Next We Have the Most Important Property Of (12)mentioning
confidence: 99%
“…Hidden normally hyperbolic manifolds as described above frequently occur in the analysis of slow-fast systems, for example in the context of biochemical oscillations see [17], [18]. However, a general treatment of such scenario is not available.…”
Section: Next We Have the Most Important Property Of (12)mentioning
confidence: 99%
“…Recursive blow ups can (and have been) used to further desingularize the vector field. This technique has been successfully used not only to study local trajectories but also to get quantitative results on the passage of trajectories close to singularities [46].…”
Section: Rescaling and Blow Upmentioning
confidence: 99%