By Alain Oustaloup

In accordance with a based method of range, significantly encouraged by way of a number of varieties of variety of common origins, variety and Non-integer Derivation utilized to approach Dynamics presents a research framework to the advent of the non-integer spinoff as a modeling software. Modeling instruments that spotlight unsuspected dynamical performances (notably damping performances) in an "integer" method of mechanics and�Read more...

summary: in accordance with a based method of range, significantly encouraged by way of numerous types of variety of ordinary origins, variety and Non-integer Derivation utilized to method Dynamics offers a examine framework to the creation of the non-integer by-product as a modeling instrument. Modeling instruments that spotlight unsuspected dynamical performances (notably damping performances) in an "integer" strategy of mechanics and automation also are integrated. Written to allow a two-tier analyzing, this can be an important source for scientists, researchers, and commercial engineers drawn to this topic a

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**Additional info for Diversity and Non-integer Differentiation for System Dynamics**

**Sample text**

The study object To support the proceedings of our strategy, we have chosen a natural study system, though stylized, as for the representation. This study object (or system) is certainly no stranger to the damping properties of the highly disturbed (or uneven) dykes, notably those forming air pockets compressible by water advance. 5) is motion water of mass M which (horizontally) relaxes on a porous dyke whose pore localization is here reduced to the face (Appendix 2). 5. Study object From Diversity to Unexpected Dynamic Performances 7 It is then a porous face replying, besides, to multiplicity by its pore number that achieves the water-dyke interface.

15. 1. 4] from which m is directly deduced, namely: m= log α . 16. 2. 8] a relation that expresses that non-integer derivative models the porous face. The model parametric compacity (or parsimony) is proven by two parameters, the differentiation non-integer order m and the unit gain frequency ω 0 . 3. 10] From Diversity to Unexpected Dynamic Performances 15 αj λ −1s , R λ −1s + λ jω 0 = α ∑ j∈ namely, from Y ( s ) expressed by the sum on i : ( ) Y ( s ) = αY λ −1s . 11] Ks m being relative to the smoothing and X ( s ) being relative to the gain and phase undulations around the smoothing straight lines ( X ( s ) tending toward 1 when λ tends toward 1), we attribute to the admittance Y ( s) a general expression of the form: Y ( s) = Ks m X ( s) .

This circuit is achieved in such a way that its transmittance presents, in a medium frequency band, a denominator in conformity with the characteristic polynomial of the non-integer differential equation which governs the water relaxation on a porous dyke. 2. From ladder network to a non-integer derivative as a water-dyke interface model The ladder network is nothing but the recursive parallel arrangement of series RC cells that represents the hydropneumatic model of the porous face (or the waterdyke interface).