English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Quaternion kinematical differential equation (QKDE) plays a key role innavigation, control and guidance systems. Although explicit symplecticgeometric algorithms (ESGA) for this problem are available, there is a lack ofa unified way for constructing high order symplectic difference schemes withconfigurable order parameter. We present even order explicit symplecticgeometric algorithms to solve the QKDE with diagonal Pad\`{e} approximation andCayley transform. The maximum absolute error for solving the QKDE is$\mathcal{O}(\tau^{2\ell})$ where $\tau$ is the time step and $\ell$ is theorder parameter. The linear time complexity and constant space complexity ofcomputation as well as the simple algorithmic structure show that ouralgorithms are appropriate for realtime applications in aeronautics,astronautics, robotics, visual-inertial odemetry and so on. The performance ofthe proposed algorithms are verified and validated by mathematical analysis andnumerical simulation.

Even Order Explicit Symplectic Geometric Algorithms for Quaternion  Kinematical Differential Equation in Guidance Navigation and Control via  Diagonal Pad\`{e} Approximation and Cayley Transform