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Related Concept Videos

Kinematic Equations - II01:17

Kinematic Equations - II

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...
Kinematic Equations for Rotation01:30

Kinematic Equations for Rotation

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...
Kinematic Equations - III01:18

Kinematic Equations - III

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,...
Kinematic Equations - I01:26

Kinematic Equations - I

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:
Relative Motion Analysis using Rotating Axes01:25

Relative Motion Analysis using Rotating Axes

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 instrumental in...
Kinematic Equations: Problem Solving01:15

Kinematic Equations: Problem Solving

When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the appropriate kinematic equations to solve for the unknowns. Either one or two kinematic equations are needed to solve for the unknowns, depending on the known and unknown quantities. Generally, the number of equations required is the same as the number of unknown quantities in the given example. Two-body pursuit problems always require two...

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Related Experiment Video

Updated: Jun 9, 2026

Measuring 3D In-vivo Shoulder Kinematics using Biplanar Videoradiography
06:09

Measuring 3D In-vivo Shoulder Kinematics using Biplanar Videoradiography

Published on: March 12, 2021

A fast bilinear structure from motion algorithm using a video sequence and inertial sensors.

Mahesh Ramachandran1, Ashok Veeraraghavan, Rama Chellappa

  • 1Qualcomm Inc., 5775 Morehouse Dr., San Diego, CA 92121-1714, USA. maheshr@umiacs.umd.edu

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 25, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a fast and robust Structure from Motion (SfM) algorithm for 3D urban modeling. By incorporating camera height and vertical direction from inertial sensors, the algorithm achieves lower error and faster convergence than traditional methods.

Related Experiment Videos

Last Updated: Jun 9, 2026

Measuring 3D In-vivo Shoulder Kinematics using Biplanar Videoradiography
06:09

Measuring 3D In-vivo Shoulder Kinematics using Biplanar Videoradiography

Published on: March 12, 2021

Area of Science:

  • Computer Vision
  • Robotics
  • Geomatics

Background:

  • 3D urban modeling relies on Structure from Motion (SfM) techniques.
  • Accurate 3D reconstruction often requires additional sensor data.
  • Monocular SfM typically struggles with scale ambiguity and robustness.

Purpose of the Study:

  • To develop a novel SfM algorithm utilizing camera height and vertical direction.
  • To demonstrate the benefits of incorporating inertial sensor data into SfM.
  • To improve the speed, robustness, and accuracy of 3D urban modeling.

Main Methods:

  • Rewriting SfM equations in a bilinear form using vertical and height information.
  • Developing a fast, robust, and scalable SfM algorithm.
  • Experimental validation against sparse bundle adjustment.

Main Results:

  • The proposed SfM algorithm converges to solutions with lower error than state-of-the-art bundle adjustment.
  • The algorithm demonstrates faster convergence times for large-scale reconstruction problems.
  • Successful SfM reconstruction on the Google StreetView dataset.

Conclusions:

  • Integrating camera height and vertical direction significantly enhances SfM performance.
  • The developed SfM algorithm offers a superior alternative for large-scale 3D urban modeling.
  • The method shows promise for real-world applications using monocular video and inertial sensors.