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Velocity and position can be calculated from the known function of acceleration as a function of time. The total area under the acceleration-time graph and the velocity-time graph gives the change in velocity and position, respectively. In the case of an airplane, its acceleration is tracked using the inertial navigation system. The pilot provides the input of the airplane's initial position and velocity before takeoff. The inertial navigation system then uses the acceleration data to...
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To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position needs to be specified relative to a convenient frame of reference. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference to describe the position of an object in relation to stationary objects on Earth.
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A displacement current is analogous to a real current in Ampère's law, participating in Ampère's law the same way as the usual conduction current. However, it is produced by a changing electric field. Displacement current is defined in terms of a time-varying electric field, and also has an associated displacement current density. By adding a term accounting for displacement current, Maxwell modified the existing Ampère's law, which is now called generalized Ampère's law.
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Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.
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Related Experiment Video

Updated: Jan 3, 2026

Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling
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Efficacy of Msplit Estimation in Displacement Analysis.

Zbigniew Wiśniewski1, Robert Duchnowski1, Andrzej Dumalski1

  • 1Institute of Geodesy, University of Warmia and Mazury in Olsztyn, 1 Oczapowskiego St., 10-957 Olsztyn, Poland.

Sensors (Basel, Switzerland)
|November 23, 2019
PubMed
Summary

Msplit estimation offers an alternative to conventional methods for analyzing geodetic observations. This method automatically assigns observations to functional models, proving effective in detecting point displacements, especially in disordered datasets.

Keywords:
Monte Carlo simulationsMsplit estimationdeformation analysisefficacy

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Area of Science:

  • Geodesy and Geophysics
  • Geodetic observation analysis
  • Deformation analysis

Background:

  • Geodetic observation sets often contain data with differing functional models or parameter values.
  • Conventional methods like least squares estimation require pre-separation of observation subsets.
  • Analyzing observations from various measurement epochs presents challenges for traditional approaches.

Purpose of the Study:

  • To evaluate the efficacy of Msplit estimation for detecting point displacements in geodetic data.
  • To compare Msplit estimation with classical deformation analysis methods.
  • To investigate the performance of Msplit estimation on disordered observation sets.

Main Methods:

  • Application of Msplit estimation, which assigns each observation to competitive functional models automatically.
  • Utilizing example geodetic observation sets.
  • Conducting Monte Carlo simulations to assess performance.
  • Comparing results with classical deformation analysis.

Main Results:

  • Msplit estimation demonstrates efficacy in detecting point displacements.
  • The method shows promise as an alternative to conventional geodetic data analysis techniques.
  • Msplit estimation exhibits a distinct advantage over conventional approaches for disordered observation sets.

Conclusions:

  • Msplit estimation is a viable and potentially advantageous alternative for deformation analysis in geodesy.
  • The automatic assignment of observations to functional models simplifies the analysis process.
  • The method's effectiveness is particularly notable in scenarios with disordered observational data.