Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Relative Motion Analysis using Rotating Axes-Problem Solving

Relative Motion Analysis using Rotating Axes-Problem Solving

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...

Reduced Mass Coordinates: Isolated Two-body Problem

Reduced Mass Coordinates: Isolated Two-body Problem

In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...

Kinematic Equations: Problem Solving

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...

Equation of Motion: General Plane motion - Problem Solving

Equation of Motion: General Plane motion - Problem Solving

Consider a lawn roller with a mass of 100 kg, a radius of 0.2 meters, and a radius of gyration of 0.15 meters. A force of 200 N is applied to this roller, angled at 60 degrees from the horizontal plane. What will be the angular acceleration of the lawn roller?
The friction between the roller and the ground is characterized by two coefficients. The static friction coefficient is 0.15, while the kinetic friction coefficient is 0.1. These values are crucial in understanding the interaction between...

Kinematic Equations - III

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,...

Equation of Motion for a Rigid Body

Equation of Motion for a Rigid Body

The movement of a rigid object can be understood through the equations that explain both translational and rotational motion about the center of mass of the object, point G. This center of mass is the point where the equation of motion for translational motion comes into play, as per Newton's Second Law.
The combined moments generated about the center of mass of the object are equal to the rate of change of the angular momentum of the body. An external force, when applied at a different point...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Possible daily and seasonal variations in quantum interference induced by Chern-Simons gravity.

Physical review letters·2013

Same author

Gravitational wave forms for two- and three-body gravitating systems.

Physical review letters·2009

See all related articles

Search research articles

Related Experiment Video

Updated: Jul 13, 2026

Three-Dimensional Mapping of the Rotation of Interactive Virtual Objects with Eye-Tracking Data

Three-Dimensional Mapping of the Rotation of Interactive Virtual Objects with Eye-Tracking Data

Published on: October 18, 2024

Choreographic solution to the general-relativistic three-body problem.

Tatsunori Imai¹, Takamasa Chiba, Hideki Asada

¹Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan.

Physical Review Letters

|August 7, 2007

Summary

General relativity

Area of Science:

Celestial Mechanics
Astrophysics
General Relativity

Background:

The Newtonian N-body problem allows for choreographic solutions, where all bodies follow identical periodic orbits.
A notable example is the figure-eight orbit for three bodies, proven to exist by Chenciner and Montgomery.
General relativity's periastron shift complicates closed orbits in binary systems, raising questions about choreographic solutions.

Purpose of the Study:

To investigate whether choreographic solutions, specifically the figure-eight orbit, are possible within the framework of general relativity.
To determine if general-relativistic effects permit such periodic, identical orbits for multiple bodies.

Main Methods:

Examining general-relativistic corrections to initial conditions for a three-body system.

More Related Videos

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions

Published on: May 10, 2012

Controlled Rotation of Human Observers in a Virtual Reality Environment

Controlled Rotation of Human Observers in a Virtual Reality Environment

Published on: April 21, 2022

Related Experiment Videos

Last Updated: Jul 13, 2026

Three-Dimensional Mapping of the Rotation of Interactive Virtual Objects with Eye-Tracking Data

Three-Dimensional Mapping of the Rotation of Interactive Virtual Objects with Eye-Tracking Data

Published on: October 18, 2024

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions

Published on: May 10, 2012

Controlled Rotation of Human Observers in a Virtual Reality Environment

Controlled Rotation of Human Observers in a Virtual Reality Environment

Published on: April 21, 2022

Analyzing how relativistic effects modify orbital paths compared to Newtonian mechanics.

Main Results:

The study suggests that general-relativistic effects can be accounted for to achieve choreographic, figure-eight-like orbits.
Corrections to initial conditions are proposed to enable these specific types of periodic motion.

Conclusions:

General-relativistic choreographic solutions, including figure-eight orbits, may exist under specific initial conditions.
This research extends the possibility of choreographic solutions to the realm of general relativity.