Gravitation Two-Body System. Gravitation m1m1 m2m2 F 12 F 21.

Slides:

Advertisements

Similar presentations

CHS Physics Motion in Two and Three Dimensions. Position  The position of an object in two or three dimensions is given by a position vector.  The vector.

Advertisements

Conservative vs. Non-conservative Forces

Summer School 2007B. Rossetto1 5. Kinematics  Piecewise constant velocity t0t0 tntn titi t i+1 x(t) x(t i ) h t x i = v(t i ). h Distance runned during.

13.1 Newton’s law of motion 1.Newton’s 2 nd law of motion (1) A particle subjected to an unbalanced force experiences an accelerationhaving the same direction.

PHYS16 – Lecture 21 Circular Motion October 27, 2010.

Classical Mechanics. Newton’s First Law The Law of Inertia The NATURAL state of motion is to resist changes.

Problem Solving For Conservation of Momentum problems: 1.BEFORE and AFTER 2.Do X and Y Separately.

Test 3 today, at 7 pm and 8:15 pm, in Heldenfels 109 Chapters

Euler Rotation. Angular Momentum  The angular momentum J is defined in terms of the inertia tensor and angular velocity. All rotations included  The.

Chapter 11 Rolling, Torque, and Angular Momentum In this chapter we will cover the following topics: -Rolling of circular objects and its relationship.

Spacecraft Dynamics and Control

Conservation of Momentum

Central Forces. Two-Body System  Center of mass R  Equal external force on both bodies.  Add to get the CM motion  Subtract for relative motion m2m2.

Newton’s Laws of Motion and Planetary Orbits Gravity makes the solar system go round.

GRAPHS  INTERPRET  MEASURE SLOPE  -INSATATANEOUS AND AVERAGE  MEASURE AREA.

Define force What is the difference between a balanced force and unbalanced force? What is the net force? How do you combine forces?

Stanford University Department of Aeronautics and Astronautics Introduction to Symmetry Analysis Brian Cantwell Department of Aeronautics and Astronautics.

Osculating Circles and Trajectories Just Kidding.

9/7/2012PHY 711 Fall Lecture 51 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 5: 1.Chapter 2 –

Physics 311 Classical Mechanics Welcome! Syllabus. Discussion of Classical Mechanics. Topics to be Covered. The Role of Classical Mechanics in Physics.

© Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion.

Copyright Kaplan AEC Education, 2005 Dynamics Outline Overview DYNAMICS, p. 193 KINEMATICS OF A PARTICLE, p. 194 Relating Distance, Velocity and the Tangential.

Kinetic energy Derivation of kinetic energy. Kinetic Energy 2 starting equations F = m x a (Newton’s 2 nd law) W = Force x distance.

Two-Body Systems.

Quiz Chapter 3  Law of Gravitation  Rectangular Components  Law of Inertia and Equilibrium  Position Vectors  Angular Positions.

Motion Summary.  Vectors & Scalars  Displacement, Velocity, Acceleration  Equations of motion  Relative motion.

Jump to first page Chapter 4 Kinetics of a Particle xx f(x)f(x) x ff max min.

Jump to first page 1 Chapter 3 Kinematics of particles Differentiation: the ratio between two increments when they are extremely small, e.g. velocity.

Relativity Discussion 4/19/2007 Jim Emery. Einstein and his assistants, Peter Bergmann, and Valentin Bargmann, on there daily walk to the Institute for.

Chapter 7: Linear Momentum Along with conservation of energy, we will now include other conserved quantities of linear and angular momentum. Linear momentum.

Impulse and Momentum Impulse and momentum stem from Newton’s Second Law: Impulse (FΔt): The product of the force and the time it acts on an object. (N·s)

Chapter 12 KINETICS OF PARTICLES: NEWTON’S SECOND LAW Denoting by m the mass of a particle, by  F the sum, or resultant, of the forces acting on the.

DYNAMICS CONTENTS.

© Fox, Pritchard, & McDonald Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion.

1 Two of Newton’s Law of Motions 1) In the absence of any forces applied, an object at rest will stay at rest, and a body moving at a constant velocity.

Differential Equations Linear Equations with Variable Coefficients.

Section 17.4 The Flow of a Vector Field. Often we are concerned with the path an object will travel We can use the information from the velocity vector.

DIFFERENTIAL EQUATIONS Note: Differential equations are equations containing a derivative. They can be solved by integration to obtain a general solution.

Newton’s Law of Universal Gravitation && Kepler’s Laws of Planetary Motion.

Oscillations Readings: Chapter 14.

PHYSICS 361 (Classical Mechanics) Dr. Anatoli Frishman Web Page:

Physics 111 Lecture Summaries (Serway 8 th Edition): Lecture 1Chapter 1&3Measurement & Vectors Lecture 2 Chapter 2Motion in 1 Dimension (Kinematics) Lecture.

 The metric system – units, prefixes  Unit conversions  Algebra and trigonometry  Orders of magnitude.

Particle Kinematics Direction of velocity vector is parallel to path Magnitude of velocity vector is distance traveled / time Inertial frame – non accelerating,

9/2/2015PHY 711 Fall Lecture 41 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 4: Chapter 2 – Physics.

Dynamics FE Review Session Adapted from the following references:

Essential Questions: 1. How do forces affect the motion of an object?

< initial velocity of Object B > initial velocity of Object B

Vector-Valued Functions and Motion in Space

PHY 711 Classical Mechanics and Mathematical Methods

Cylindrical – Polar Coordinates

Rotational Equilibrium and Dynamics

Section 3.5 – Curvilinear Motion

Oscillations Readings: Chapter 14.

Section Indefinite Integrals

ME321 Kinematics and Dynamics of Machines

Physics 111 Practice Problem Solutions 11 Angular Momentum SJ 8th Ed

Find the velocity of a particle with the given position function

PHY 711 Classical Mechanics and Mathematical Methods

PHY 711 Classical Mechanics and Mathematical Methods

Impulse and Momentum Readings: Chapter 9.

2-4 Acceleration Acceleration is the rate of change of velocity.

12.6: Vector Magnitude & Distance

Section 9.4 – Solving Differential Equations Symbolically

Problem A 250-g collar can slide on a 400 mm

( ) Lagrangian Control Volume < > < l < l = ( , , ) l l l

Chapter 2 - Part 1 The two body problem

Section Indefinite Integrals

Newton’s first and second laws

Introduction to Fluid Mechanics

Presentation transcript:

Gravitation Two-Body System

Gravitation m1m1 m2m2 F 12 F 21

Position - Velocity - Acceleration x y

Cartesic Coordinates x y y x

Cartesic Coordinates Velocity x y y x

Cartesic Coordinates Acceleration x y y x

Polar Coordinates x y

Polar Coordinates Changes of unit vectors x y

Polar Coordinates Velocity x y

Polar Coordinates Acceleration x y

x y

Two-Body System Newton’s Laws m1m1 m2m2 F 12 F 21

Two-Body System Reduction to one-particle problem m1m1 m2m2 F 12 F 21

Two-Body System Angular Momentum m1m1 m2m2 F 12 F 21

Two-Body System Differential Equation r m1m1 m2m2 F 12 F 21

Two-Body System Equation r, r 1, r 2 m1m1 m2m2 F 12 F 21

Two-Body System Solution of Differential Equation

Two-Body System Solution

Two-Body System Solution - Different Path

End