On the coordinate system-dependence of the accuracy of symplectic numerical methods | Paper Citation Record

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This paper cites The dynamical structure of the Kuiper belt.

On the coordinate system-dependence of the accuracy of symplectic numerical methods The dynamical structure of the Kuiper belt

Reference 1

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This paper cites The role of symplectic integrators in optimal control.

On the coordinate system-dependence of the accuracy of symplectic numerical methods The role of symplectic integrators in optimal control

Reference 2

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On the coordinate system-dependence of the accuracy of symplectic numerical methods La2010: a new orbital solution for the long-term motion of the Earth

Reference 3

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This paper cites OrbitN: A Symplectic Integrator for Planetary Systems Dominated by a Central Mass—Insight into Long-term Solar System Chaos.

On the coordinate system-dependence of the accuracy of symplectic numerical methods OrbitN: A Symplectic Integrator for Planetary Systems Dominated by a Central Mass—Insight into Long-term Solar System Chaos

Reference 4

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On the coordinate system-dependence of the accuracy of symplectic numerical methods Discrete mechanics and optimal control applied to the compass gait biped

Reference 5

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On the coordinate system-dependence of the accuracy of symplectic numerical methods Discrete mechanics and optimal control: An analysis

Reference 6

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This paper cites Simultaneous path planning and trajectory optimization for robotic manipulators using discrete mechanics and optimal control.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Simultaneous path planning and trajectory optimization for robotic manipulators using discrete mechanics and optimal control

Reference 7

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This paper cites An iterative framework to solve nonlinear optimal control with proportional delay using successive convexification and symplectic multi-interval pseudospectral scheme.

On the coordinate system-dependence of the accuracy of symplectic numerical methods An iterative framework to solve nonlinear optimal control with proportional delay using successive convexification and symplectic multi-interval pseudospectral scheme

Reference 8

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This paper cites Solar System chaos and the Paleocene–Eocene boundary age constrained by geology and astronomy.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Solar System chaos and the Paleocene–Eocene boundary age constrained by geology and astronomy

Reference 9

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This paper cites Geologically constrained astronomical solutions for the Cenozoic era.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Geologically constrained astronomical solutions for the Cenozoic era

Reference 10

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This paper cites Symplectic methods applied to the Lotka–Volterra system.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Symplectic methods applied to the Lotka–Volterra system

Reference 11

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This paper cites Operator splitting methods for the Lotka–Volterra equations.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Operator splitting methods for the Lotka–Volterra equations

Reference 12

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This paper cites Geometric integration for particle accelerators.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Geometric integration for particle accelerators

Reference 13

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This paper cites A canonical integration technique.

On the coordinate system-dependence of the accuracy of symplectic numerical methods A canonical integration technique

Reference 14

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This paper cites Canonical integrators as tracking codes (or how to integrate perturbation theory with tracking).

On the coordinate system-dependence of the accuracy of symplectic numerical methods Canonical integrators as tracking codes (or how to integrate perturbation theory with tracking)

Reference 15

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This paper cites Optimal Symplectic Approximation of Hamiltonian Flows.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Optimal Symplectic Approximation of Hamiltonian Flows

Reference 16

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Observation f15cb75c-b706-47e6-9c73-09ad2e737b23 · outbound

This paper cites Asymptotically-preserving large deviations principles by stochastic symplectic methods for a linear stochastic oscillator.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Asymptotically-preserving large deviations principles by stochastic symplectic methods for a linear stochastic oscillator

Reference 17

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Observation 196e0435-e2b9-433c-9baf-d5c0ddebb2f7 · outbound

This paper cites Strong backward error analysis of symplectic integra- tors for stochastic Hamiltonian systems.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Strong backward error analysis of symplectic integra- tors for stochastic Hamiltonian systems

Reference 18

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Observation 3e9e2bf2-774b-417e-b78b-fa7b9b4aab07 · outbound

This paper cites Structure and structure-preserving algorithms for plasma physics.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Structure and structure-preserving algorithms for plasma physics

Reference 19

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Observation 5ec41e2d-6086-404e-8568-bf2babd17ae8 · outbound

This paper cites Global energy preserving model reduction for multi- symplectic PDEs.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Global energy preserving model reduction for multi- symplectic PDEs

Reference 20

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Observation 4b5caabc-5ac9-4656-9177-d3809dda372d · outbound

This paper cites Thermodynamically extended symplectic numerical simulation of viscoelastic, thermal expansion and heat conduction phenomena in solids.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Thermodynamically extended symplectic numerical simulation of viscoelastic, thermal expansion and heat conduction phenomena in solids

Reference 21

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This paper cites Discrete energy balance equation via a symplectic second-order method for two-phase flow in porous media.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Discrete energy balance equation via a symplectic second-order method for two-phase flow in porous media

Reference 22

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This paper cites OntheHamiltonianinterpolationofnear-to-theidentitysymplectic mappingswithapplicationtosymplecticintegrationalgorithms.

On the coordinate system-dependence of the accuracy of symplectic numerical methods OntheHamiltonianinterpolationofnear-to-theidentitysymplectic mappingswithapplicationtosymplecticintegrationalgorithms

Reference 23

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Observation 177e6644-52b7-4b4d-a7b6-41fa493b3f8f · outbound

This paper cites Hairer, C.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Hairer, C

Reference 24

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This paper cites Improving the accuracy of the Newmark method through backward error analysis.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Improving the accuracy of the Newmark method through backward error analysis

Reference 25

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Observation 70ddc94e-3b02-432c-a556-0f14b081e47b · outbound

This paper cites Leimkuhler and S.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Leimkuhler and S

Reference 26

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Observation acebc4d1-41b0-4c6a-ba67-2f26080ab04f · outbound

This paper cites Feng and M.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Feng and M

Reference 27

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Observation 07a77fe3-f4ab-44f5-8249-b4f615ca3b57 · outbound

This paper cites A note on conservation laws of symplectic difference schemes for Hamiltonian systems.

On the coordinate system-dependence of the accuracy of symplectic numerical methods A note on conservation laws of symplectic difference schemes for Hamiltonian systems

Reference 28

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This paper cites Variational integrators and the Newmark algorithm for conservative and dissipa- tive mechanical systems.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Variational integrators and the Newmark algorithm for conservative and dissipa- tive mechanical systems

Reference 29

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This paper cites On modified equations for discretizations of ODEs.

On the coordinate system-dependence of the accuracy of symplectic numerical methods On modified equations for discretizations of ODEs

Reference 30

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This paper cites Monte Carlo calculation of quantum systems. II. Higher order correction.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Monte Carlo calculation of quantum systems. II. Higher order correction

Reference 31

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This paper cites A numerical algorithm for Hamiltonian systems.

On the coordinate system-dependence of the accuracy of symplectic numerical methods A numerical algorithm for Hamiltonian systems

Reference 32

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This paper cites Explicit Symplectic Integrators Using Hessian–Vector Products.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Explicit Symplectic Integrators Using Hessian–Vector Products

Reference 33

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This paper cites Splitting methods.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Splitting methods

Reference 34

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This paper cites On processed splitting methods and high-order actions in path-integral Monte Carlo simulations.

On the coordinate system-dependence of the accuracy of symplectic numerical methods On processed splitting methods and high-order actions in path-integral Monte Carlo simulations

Reference 35

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This paper cites Uber ein neues Integral für den Fall der drei Körper, wenn die Bahn des störenden Planeten kreisförmig angenommen und die Masse des gestörten vernachlässigt wird.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Uber ein neues Integral für den Fall der drei Körper, wenn die Bahn des störenden Planeten kreisförmig angenommen und die Masse des gestörten vernachlässigt wird

Reference 36

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This paper cites The Early History of Hamilton-Jacobi Dynamics 1834–1837.

On the coordinate system-dependence of the accuracy of symplectic numerical methods The Early History of Hamilton-Jacobi Dynamics 1834–1837

Reference 37

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On the coordinate system-dependence of the accuracy of symplectic numerical methods Unresolved cited work

Reference 38

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This paper cites Goldstein, C.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Goldstein, C

Reference 39

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This paper cites Hairer and G.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Hairer and G

Reference 40

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Observation 429751d3-79b8-4a9c-b967-3e546b324441 · outbound

This paper cites On the convergence of multistep methods for nonlinear stiff differential equations.

On the coordinate system-dependence of the accuracy of symplectic numerical methods On the convergence of multistep methods for nonlinear stiff differential equations

Reference 41

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Observation 9e748e22-e4fd-4ce4-b9e6-cf9dacd92d95 · outbound

This paper cites On the Scope of the Method of Modified Equations.

On the coordinate system-dependence of the accuracy of symplectic numerical methods On the Scope of the Method of Modified Equations

Reference 42

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Observation 31975b16-59cc-4afa-8692-e40ef3e3fc5e · outbound

This paper cites Cheap enhancement of symplectic integrators.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Cheap enhancement of symplectic integrators

Reference 43

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This paper cites Backward error analysis for numerical integrators.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Backward error analysis for numerical integrators

Reference 44

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This paper cites Asymptotic Expansions and Backward Analysis for Numerical Inte- grators.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Asymptotic Expansions and Backward Analysis for Numerical Inte- grators

Reference 45

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This paper cites Gompertz.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Gompertz

Reference 46

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This paper cites The Gompertz curve as a growth curve.

On the coordinate system-dependence of the accuracy of symplectic numerical methods The Gompertz curve as a growth curve

Reference 47

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This paper cites The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the Unified-Richards family.

On the coordinate system-dependence of the accuracy of symplectic numerical methods The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the Unified-Richards family

Reference 48

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This paper cites Models of cancer growth.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Models of cancer growth

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:45:34.936848Z

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Observation 2ef46745-b57b-4e44-b158-13c77b2ccbbc · outbound

This paper cites de Vogelaere.Methods of integration which preserve the contact transformation property of the Hamilton equations.

On the coordinate system-dependence of the accuracy of symplectic numerical methods de Vogelaere.Methods of integration which preserve the contact transformation property of the Hamilton equations

Reference 50

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Observation 1c53831e-545a-48f8-a936-f2268073eeb4 · outbound

This paper cites Partitioned second derivative methods for separable Hamiltonian problems.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Partitioned second derivative methods for separable Hamiltonian problems

Reference 51

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This paper cites The effective order of Runge–Kutta methods.

On the coordinate system-dependence of the accuracy of symplectic numerical methods The effective order of Runge–Kutta methods

Reference 52

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Observation a44d2d37-4a1b-440d-8d15-715ea8f10f06 · outbound

This paper cites Symplectic correctors.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Symplectic correctors

Reference 53

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Observation 1fac52d7-c823-43f5-bfe8-b21ff8731913 · outbound

This paper cites Farzaneh, ed.Atmospheric Icing of Power Networks.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Farzaneh, ed.Atmospheric Icing of Power Networks

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:45:33.812615Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4dac656f-712c-473c-9ba0-b06be7522068 · outbound

This paper cites Ice-shedding-induced vibration of conductors with active vibration control.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Ice-shedding-induced vibration of conductors with active vibration control

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-06T22:45:27.744275Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9686e85d-a014-4562-82f3-9ab9e68ded50 · outbound

This paper cites Domains of Attraction of System of Nonlinearly Coupled Ship Motions by Simple Cell Mapping.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Domains of Attraction of System of Nonlinearly Coupled Ship Motions by Simple Cell Mapping

Reference 56

Resolution: verified exact; doi, observed 2026-08-06T22:45:30.232307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4082ac13-ee0b-4217-82dc-cb21025de9e7 · outbound

This paper cites Chaotic dynamics of a harmonically excited spring-pendulum system with internal resonance.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Chaotic dynamics of a harmonically excited spring-pendulum system with internal resonance

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:45:33.690407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 88967466-45b5-4331-ae91-0269a6e7b675 · outbound

This paper cites Order Conditions for Canonical Runge–Kutta Schemes.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Order Conditions for Canonical Runge–Kutta Schemes

Reference 58

Resolution: verified exact; doi, observed 2026-08-06T22:45:29.918011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8d00e8cd-9f6a-4e50-818e-b8aa5025c359 · outbound

This paper cites Backward analysis of numerical integrators and symplectic methods.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Backward analysis of numerical integrators and symplectic methods

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:45:33.533187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0140270e-a38e-4007-9f67-5046f1c21c2b · outbound

This paper cites Hairer, S.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Hairer, S

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:45:33.383789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c9b81db5-dbbb-4ac9-9870-51d6aec797f8 · outbound

This paper cites Runge-Kutta schemes for Hamiltonian systems.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Runge-Kutta schemes for Hamiltonian systems

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-06T22:45:28.360922Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 68a8dd19-fffc-460f-8660-a0f3b56c3475 · outbound

This paper cites Canonical B-series.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Canonical B-series

Reference 62

Resolution: verified exact; doi, observed 2026-08-06T22:45:29.611417Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 3cb0f518-6df6-44dd-ad22-26ab4ad6c80d · outbound

This paper cites An Algebraic Approach to Invariant Preserving Integators: The Case of Quadratic and Hamiltonian Invariants.

On the coordinate system-dependence of the accuracy of symplectic numerical methods An Algebraic Approach to Invariant Preserving Integators: The Case of Quadratic and Hamiltonian Invariants

Reference 63

Resolution: verified exact; doi, observed 2026-08-06T22:45:29.379693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation da7d5bd0-6db0-4c46-988b-f316c85ad2e0 · outbound

This paper cites McDuff and D.

On the coordinate system-dependence of the accuracy of symplectic numerical methods McDuff and D

Reference 64

Resolution: unresolved; no resolver link, observed 2026-08-06T22:45:28.672072Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ccc2c343-d528-470e-b4e1-c14ac3172857 · outbound

This paper cites Walter.Astronautics: The Physics of Space Flight.

On the coordinate system-dependence of the accuracy of symplectic numerical methods Walter.Astronautics: The Physics of Space Flight

Reference 65

Resolution: verified exact; doi, observed 2026-08-06T22:45:29.044893Z

Source-reported events for the cited work

correction dated 2019-10-30. Source: crossref record 10.1007/978-3-319-74373-8_17->10.1007/978-3-319-74373-8:correction, observed 2026-07-11T03:05:50.43548+00:00. This notice travels one citation hop only.

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