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Related Concept Videos

Kinematic Equations for Rotation01:30

Kinematic Equations for Rotation

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In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
For instance, imagine a point A on a rigid body engaged in circular motion. The translational velocity of this particular point can be calculated by taking the time derivatives of the displacement equation, which essentially measures the...
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Kinematic Equations - I01:26

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When an object moves with constant acceleration, the velocity of the object changes at a constant rate throughout the motion. The kinematic equations of motions are derived for such cases where the acceleration of the object is constant. The first kinematic equation gives an insight into the relationship between velocity, acceleration, and time. We can see, for example:
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Kinematic Equations - III01:18

Kinematic Equations - III

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The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity as a function of the acceleration and distance over which it acts. The fourth kinematic equation does not have an acceleration term and provides the final position of the object at time t in terms of the initial and final velocities. This equation is useful when the value of the constant acceleration is unknown.
Using the kinematic equations,...
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Relative Motion Analysis using Rotating Axes-Problem Solving01:29

Relative Motion Analysis using Rotating Axes-Problem Solving

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Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
Here, in order to determine the magnitude of velocity and acceleration for point...
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Kinematic Equations - II01:17

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The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant velocity, and the distance traveled due to a change in velocity. Similar to the first kinematic equation, this equation is also only valid when the acceleration is constant throughout the motion of an object.
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...
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Relative Motion Analysis using Rotating Axes01:25

Relative Motion Analysis using Rotating Axes

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Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.
However, to express the relative position of point B relative to point A, an additional frame of reference, denoted as x'y', is necessary. This additional frame not only translates but also rotates relative to the fixed frame, making it...
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Related Experiment Video

Updated: Mar 15, 2026

An Inertial Measurement Unit Based Method to Estimate Hip and Knee Joint Kinematics in Team Sport Athletes on the Field
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A Direct and Non-Singular UKF Approach Using Euler Angle Kinematics for Integrated Navigation Systems.

Changyan Ran1,2,3, Xianghong Cheng4,5

  • 1School of Instrument Science & Engineering, Southeast University, Nanjing 210096, China. ranchangyan@126.com.

Sensors (Basel, Switzerland)
|September 7, 2016
PubMed
Summary

This study introduces a direct, non-singular method using an unscented Kalman filter (UKF) for strapdown inertial navigation systems (SINSs) aided by velocity measurements. This approach enhances navigation accuracy and effectively removes singularities for improved performance.

Keywords:
Euler angle kinematicsintegrated navigationsingularitystrapdown inertial navigation system (SINS)unscented Kalman filters (UKF)

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Area of Science:

  • Navigation Systems Engineering
  • Control Theory
  • Signal Processing

Background:

  • Strapdown inertial navigation systems (SINSs) are crucial for autonomous navigation but suffer from drift and potential singularities.
  • Traditional integration methods often require separate navigation computation and error correction, increasing complexity.
  • Velocity aiding is a common technique to improve SINS accuracy, but its integration can be challenging.

Purpose of the Study:

  • To develop a direct and non-singular integration approach for velocity-aided SINS.
  • To eliminate quaternion constraints and cross-noise issues inherent in some SINS integration methods.
  • To achieve synchronous navigation computation and direct output of navigation information.

Main Methods:

  • Utilized an unscented Kalman filter (UKF) for direct data fusion.
  • Employed a state vector including velocity and Euler angles with Euler angle kinematics.
  • Implemented a dual-Euler method to avoid singularities and used body-frame velocity measurements.

Main Results:

  • The proposed UKF-based approach demonstrated higher navigation accuracy compared to indirect methods.
  • Singularities were effectively avoided, as confirmed by dedicated singularity turntable tests.
  • The method simplified the integration process by performing synchronous navigation computation.

Conclusions:

  • The direct, non-singular UKF approach offers a robust and accurate solution for velocity-aided SINS.
  • The dual-Euler method successfully mitigates singularity issues, enhancing system reliability.
  • This method provides a simplified and efficient alternative for SINS integration.