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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.
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Related Experiment Video

Updated: Nov 19, 2025

Robotic Mirror Therapy System for Functional Recovery of Hemiplegic Arms
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Solving Complex-Valued Time-Varying Linear Matrix Equations via QR Decomposition With Applications to Robotic Motion

Vasilios N Katsikis, Spyridon D Mourtas, Predrag S Stanimirovic

    IEEE Transactions on Neural Networks and Learning Systems
    |January 29, 2021
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel method for solving complex-valued time-varying linear matrix equations using QR decomposition. The proposed model effectively handles various linear systems and demonstrates utility in robotics and signal processing applications.

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    Area of Science:

    • Numerical Analysis
    • Computational Science
    • Applied Mathematics

    Background:

    • Linear matrix equations are fundamental in science and engineering.
    • Solving complex-valued time-varying linear matrix equations (CVTV-LME) presents unique challenges.

    Purpose of the Study:

    • To investigate and propose a new model for solving CVTV-LME problems.
    • To develop a robust method applicable to both square and rectangular coefficient matrices.

    Main Methods:

    • Utilized complex-valued, time-varying QR (CVTVQR) decomposition.
    • Employed zeroing neural network (ZNN) methods, equivalent transformations, Kronecker product, and vectorization techniques.
    • Developed a CVTVQR decomposition-based linear matrix equation (CVTVQR-LME) model.

    Main Results:

    • The CVTVQR-LME model effectively solves CVTV-LME problems.
    • The model demonstrates versatility by handling systems with square or rectangular coefficient matrices.
    • Numerical simulations confirmed the model's efficacy.

    Conclusions:

    • The proposed CVTVQR-LME model offers an efficient solution for complex-valued time-varying linear matrix equations.
    • The model's applicability was validated through simulations and real-world applications in robotics and angle-of-arrival localization.