ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • elliptic functions  (3)
  • 04.08. Volcanology
  • Analytical Chemistry and Spectroscopy
  • Molecular Sequence Data
  • autonomous platform; DATE/TIME; EuroSea; Improving and Integrating European Ocean Observing and Forecasting Systems for Sustainable use of the Oceans; netCDF file; netCDF file (File Size); SAILDRONE; SAILDRONE Gen6 Explorer USV; SD_1079-track
  • Springer  (3)
Collection
Keywords
Publisher
Years
  • 1
    Electronic Resource
    Electronic Resource
    Stochastic averaging using elliptic functions to study nonlinear stochastic systems (1993)
    Springer
    Nonlinear dynamics 4 (1993), S. 373-387 
    Details
    ISSN: 1573-269X
    Keywords: Stochastic averaging ; nonlinear systems ; elliptic functions ; probability density
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, a new scheme of stochastic averaging using elliptic functions is presented that approximates nonlinear dynamical systems with strong cubic nonlinearities in the presence of noise by a set of Itô differential equations. This is an extension of some recent results presented in deterministic dynamical systems. The second order nonlinear differential equation that is examined in this work can be expressed as % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qeguuDJXwAKbacfiGaf8hEaGNbamaacqGHRaWkcaWGJbadcaaIXaGc% cqWF4baEcqGHRaWkcaWGJbadcaaIZaGccqWF4baEdaahaaWcbeqaai% aaiodaaaGccqGHRaWkcqaH1oqzcaWGMbGaaiikaiab-Hha4jaacYca% cqWFGaaicuWF4baEgaGaaiaacMcacqGHRaWkcqaH1oqzdaahaaWcbe% qaaiaaigdacaGGVaGaaGOmaaaaruWrL9MCNLwyaGGbcOGaa43zaiaa% cIcacqWF4baEcaGGSaGae8hiaaIaf8hEaGNbaiaacaGGSaGae8hiaa% IaeqOVdGNaaeikaiaadshacaqGPaGaaiykaiabg2da9iaaicdaaaa!645D!\[\ddot x + c1x + c3x^3 + \varepsilon f(x, \dot x) + \varepsilon ^{1/2} g(x, \dot x, \xi {\text{(}}t{\text{)}}) = 0\] where c 1 and c 3 are given constants, ξ(t) is stationary stochastic process with zero mean and ε≪1 is a small parameter. This method involves the laborious manipulation of Jacobian elliptic functions such as cn, dn and sn rather than the usual trigonometric functions. The use of a symbolic language such as Mathematica reduces the computational effort and allows us to express the results in a convenient form. The resulting equations are Markov approximations of amplitude and phase involving integrals of elliptic functions. Finally, this method was applied to study some standard second order systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00120672
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    The Method of Averaging for Euler's Equations of Rigid Body Motion (1997)
    Springer
    Nonlinear dynamics 14 (1997), S. 295-308 
    Details
    ISSN: 1573-269X
    Keywords: Spacecraft attitude motion ; method of averaging ; elliptic functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We formulate the method of averaging for perturbations of Euler's equations of rotational motion. Euler's equations are three strongly nonlinear coupled differential equations that can be viewed as a three dimensional oscillator. The method of averaging is used to determine the long-term influence of perturbation terms on the motion by averaging about the nominal rigid body motion. The treatment is applicable to a large class of motions including precession with large nutation – it is not restricted to small motions about simple spins or nearly axi-symmetric bodies. Three examples are shown that demonstrate the accuracy of the method's predictions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008215327247
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Chaos in a system with a periodically disappearing separatrix (1990)
    Springer
    Nonlinear dynamics 1 (1990), S. 401-420 
    Details
    ISSN: 1573-269X
    Keywords: Chaos ; perturbation methods ; elliptic functions ; differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate the system $$\ddot x - x\cos \varepsilon 1 + x^3 = 0$$ in which ε≪1 by using averaging and elliptie functions. It is shown that this system is applicable to the dynamics of the familiar rotating-plane pendulum. The slow foreing permits us to envision an ‘instantancous phase portrait’ in the $$x - \dot x$$ phase plane which exhibits a center at the origin when cos ε1≤0 and a saddle and associated double homoclinic loop separatrix when cos ɛ 1 〉 0. The chaos in this problem is related to the question of on which side (left (=L) or right (=R)) of the reappearing double homoclinic loop separatrix a motion finds itself. We show that the sequence of L's and R's exhibits sensitive dependence on initial conditions by using a simplified model which assumes that motions cross the instantancous separatrix instantancously. We also present an improved model which ‘patches’ a separatrix boundary layer onto the averaging model. The predictions of both models are compared with the results of numerical integration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01893171
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...