What is Classical mechanics: Definition and 1000 Discussions
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility).
The earliest development of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on foundational works of Sir Isaac Newton, and the mathematical methods invented by Gottfried Wilhelm Leibniz, Joseph-Louis Lagrange, Leonhard Euler, and other contemporaries, in the 17th century to describe the motion of bodies under the influence of a system of forces. Later, more abstract methods were developed, leading to the reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances, made predominantly in the 18th and 19th centuries, extend substantially beyond earlier works, particularly through their use of analytical mechanics. They are, with some modification, also used in all areas of modern physics.
Classical mechanics provides extremely accurate results when studying large objects that are not extremely massive and speeds not approaching the speed of light. When the objects being examined have about the size of an atom diameter, it becomes necessary to introduce the other major sub-field of mechanics: quantum mechanics. To describe velocities that are not small compared to the speed of light, special relativity is needed. In cases where objects become extremely massive, general relativity becomes applicable. However, a number of modern sources do include relativistic mechanics in classical physics, which in their view represents classical mechanics in its most developed and accurate form.
Homework Statement
A small ball is attached to a massless string of length L, the other end of which is attached to a very thin pole. The ball is thrown so that it initially travels in a horizontal circle, with the string making an angle \theta_0 with the vertical. As time goes on, the string...
Howdy!
I am taking Phyiscs GRE next semester and won't have taken classical mechanics by the time I take the test. I am not comfortable with the situation. Can anyone please suggest me a good preparation strategy for me ?
Homework Statement
Give the equations of motion of the following system:
http://www.jelp.org/imagenes/mech.jpgHomework Equations
So, i assume the following cases (the diagram i so deficient).
1) Black Point (x1) is fixed
2) There's a force applied at x1 (black dot)
3) The position of the...
So everyone here already knows how important understanding classical mechanics is so that brings me to my question; What is a good introductory mechanics book that has nice complete mathematical derivations, good well-written physics explanation, and large breadth in terms of subject matter. In...
Hey guys, I am an undergraduate junior physics major currently enrolled in PHY3220 (Classical Mechanics) and we are using the textbook by Fowles and Cassiday titled, "Analytical Mechanics." However, I am looking for a second Classical Mechanics textbook that I could use as a reference since...
Homework Statement
How could u find the drag/friction due to air on a A4 size page dropped perpendicular to the ground. There are about 20 sheets and is dropped about waist height. The tricky thing is no instruments are aloud. Only your senses...
Homework Equations
F=-cv where c is...
Hello all, I'm having trouble with the following problem:
Pb: A chain with constant density and infinite length is slipping down from the table without friction. Determine the position of the tip of the chain at time t.
I know there are a few ways to approaching this problem, namely from...
Homework Statement
Hi all.
We have that the work W equals Ui - Uf (respectively the initial and final potential energy). Let us say that a stone has a height 10 m, and falls down. We say that positive x is upwards.
Now W = \int F \cdot dl = F(x_f-x_i)=U_f-U_i, since F and dl both point...
I'll take classical mechanics next semester and I want a book for this course. I choose two books but, unfortunately, I can buy only one, Kibble or Goldstein. I know Goldstein is going to be better but Kibble's book is much cheaper (17 pounds @ amazon.com). Does Goldstein worth it? Could you...
Homework Statement
An object is moving in one-dimensional space with a potential funciton V(x) = constant. Find the equation of motion, x(t). Use x_0 as the initial position and v_0 as the initial velocity at t=0.
Homework Equations
initial position = x_0
initial velocity = v_0
The Attempt...
Hi,
I'm looking for a good classical mechanics text for self study, roughly around my level.
So far I've taken courses in calculus based physics courses, ( first year mechanics and E&M )
multi-variable calculus, ODE's and linear algebra. I have self taught myself real analysis, and a...
Homework Statement
A disk moves on an inclined plane, with the constraint that it's velocity is always at the same direction as it's plane (similar to an ice skate, maybe). In other words: If \hat{n} is a vector normal to the disk's plane, we have at all times: \hat{n} \cdot \vec{v} = 0. Also...
Homework Statement
Consider a rocket subject to a linear resistive force, f= -bv but no other external forces. Using the equation mv'= -m'*vext+Fext show that if the rocket starts from rest and efects mass at a constant rate k= -m' then its speed is given by v=(k/b)vex[1-(m/m0)^b/k]
The...
1. The mass of the sun is decreasing as dM/dt=-constant .M
Find [dr/dt]/r for the earth
Homework Equations
[b]3. I tried using M=M0-alpha. t and then separating the variables in the equation GMm/r^2=mdv/dt. I don't knot the right way to solve this. Plz tell me how to solve this...
Homework Statement
THis time it is rather 3 problems, you are required to solve two of them before tackling third.
So, in the first problem is about hoffman transfe. YOu are asked to calculate the velocity of the spaceship when it leaves the Earth and at it's encounter with juputer. It...
[b]1. It is problem for kibble book, classical mechanics. I star with mass M traves through cloud of particles with density ro. Particles that collide with a star are trapped by it. Derive the expression for mass increase of the star dM/dt.
The Attempt at a Solution
Since all particles that...
Homework Statement
a rocket propelled car has total mass m0 and empty mass (after all of the fuel is burned) of m1. the car's exhaust speed is u and it has a constant burn rate of a=-dm/dt. ignore friction of wheels on the road, assume road is horizontal, and ignore air res. the driver fires...
Hello:
In Classical mechanics, the lagrangian of a system is defined as the kinetic energy minus the potential energy, but is there any physical meaning of the lagrangian ?, and if there is, What is it?
Regards
Homework Statement
I am self studying Chow's Classical Mechanics. I have realized that I am at my best if I leave no stone unturned
Homework Equations
\hat e_t . \hat e_t = 1
Understood
d(\hat e_t. \hat e_t)/dt =0
Also understood
But 2\hat e_t .d\hat e_t/dt=0
Not...
Dear all,
I am wondering if Introduction Classical Dynamics of Particles & Systems (5 ed.) by Marion and Thornton is any good?
I have already studied year 1 Classical Mechanics course, using University Physics by Young and Freedman.
May I know if Marion&Thornton book is of higher level and...
Homework Statement
Find the expression for the forces on support A and B. Fax, Fay, Fbx and Fby.
Homework Equations
I'm thinking;
Moment , M=F*l
Fa^2=Fax^2+Fay^2, same for b
Fax=Fbx
The Attempt at a Solution
(1) M = F*L1
Since I know that the sum of moments around the...
Hi, If these questions have been asked before, then please point me in the right direction.
1) Find the Mass of an object that is suspended by two strings. The tension on String one is 34 N and is held at a 40 degree angle with the horizontal (i.e., if a line was drawn through the center of...
I'm an EE student and I am going to take modern physics next semester, and then would like to take classical mechanics. I was enrolled for about a half week in a classical mechanics class but it seemed really hardcore and I wasn't prepared for it. (The first homework problem was: Describe the...
Hi!
This is my first post here. I'm currently studying analytical/classical mechanics and have some problems understanding how the Lie algebra is formed in relation to the SO(3) group of rotations. My problem is this:
Given a matrix representation R of some rotation around a fixed axis, we...
This is an unusual book which uses the Scheme programming language to functionally describe the various components of classical mechanics. I would say it is at the level of a graduate mechanics course (think Goldstein), however students with a strong programming background will find it easier...
[SOLVED] classical mechanics marion and thornton
Homework Statement
At the beginning of section 12.4 in marion and thornton, they say that \dot{q}_k and [itex]\ddot{q}_k[/tex] are both 0 at equilibrium, where these are generalized coordinates. Can someone please explain how they got that the...
A complete set of lecture notes for an lower-division classical mechanics course. Topics covered include one-dimensional motion, three-dimensional motion, Newton's laws of motion, energy and momentum conservation, circular and rotational motion, statics, planetary motion, oscillations, and wave...
Three equal masses arranged in a equilateral triangle are connected by 'springs' with force constants 'k'
the coordinates of the masses are:
mass 1 at [0, \sqrt{3}/2*L]
mass 2 at [L/2, 0]
mass 3 at [-L/2,0]
find the normal mode frequencies.
The only part i am having trouble with...
I will probably be taking both CM I/II and E&M I/II before I graduate, but I'm wondering is it a bad idea to take E&M before taking CM?
I don't think I can take both at the same time this coming year so I have to pick just one.
[SOLVED] Classical mechanics: ball rolling in a hollow sphere
Homework Statement
This problem is from Gregory:
A uniform ball of radius a and centre G can roll without slipping on the inside surface of a fixed hollow sphere of (inner) radius b and centre O. The ball undergoes planar...
[SOLVED] Mass on a spring
Homework Statement
This problem is from Gregory’s Classical Mechanics
A light spring of natural length a is placed on a horizontal floor in the upright position. When a block of mass M is resting in equilibrium on top of the spring, the compression of the spring...
Homework Statement
A uniform circular cylinder (a yo-yo) of radius a and mass M has a string wrapped around
it that can unwind without slipping. The yo-yo moves in a vertical straight line and the
straight part of the string is vertical as well. The other end of the string is fastened to a...
Homework Statement
Problem: Derive eigenvalue equation of motion of a system undergoing free small oscillation in three dimensional space.
Homework Equations
The Attempt at a Solution
I want to know if I have correctly written the values of T and V---
\ T=\frac{1}{2}\ m...
i'm not even sure where to get started with this one because the thorton and marion classical dynamics book is really awful.
BEGIN PROBLEM
Suppose a baseball, which has a mass of 150 g and a diameter D of 7 cm is released from rest. For a sphere in air, the dynamic drag is F_d=.25 D^2 V^2...
Homework Statement
A single particle of mass m is revolving at steady speed in a circle of radius a about the z axis at a height h above the origin. In this situation the particle has angular velocity w = wz
1 Show that the angular momentum L is not parallel to w
2 If a second particle...
Homework Statement
I need to write a C program to simulate physics problems. My job is to write a code , in which I give the user a function F(x) = ax^n + bx^(n-1) + ... , and user inputs the coefficients a,b,c ... and my computer code should tell whether the given force F(x) is conservative...
Homework Statement
My classical mechanics book (Goldstein) talks about apsidal vectors in the context of central force problems and elliptical orbits. I cannot find where the book defines this term and it is nowhere on the internet. Has anyone heard this term before?
Homework Equations...
[SOLVED] classical mechanics
Homework Statement
is it true that conjugate momentum, canonical momentum, and generalized momentum all mean the same thing (the partial of the Lagrangian with respect to the time derivative of some generalized coordinate)?
Homework Equations
The...
Speed of information – effects of on classical mechanics.
(This is not a homework or coursework question. Even if the problem stated is simple, the answer is maybe not.)
Problem: A mass is hanging vertically in a not heavy, quite inelastic and hard to compress cable which is fixed in the...
Given the Hamiltonian of a system \mathcal H , could we obtain the curves solution to Hamilton equations X(t) Y(t) Z(t) as the Geodesic of a certain surface with Christoffle symbols \Gamma ^{i} _{jk} i mean the curve X(t) satisfies the equation:
\nabla _{x(t)} X(t)=0 (covariant...
We have to show that [Lx,Ly] = Lz
[Ly,Lx] = -Lz
[Lx,Lx] = 0
and I have done this. We then need to comment on the significance of these results, which I'm not sure of. I know in QM you get similar results for commutators of these quantities, and it means that you can't simultaneously know...
Homework Statement
Any help would be much appreciated, even just a nod in the right direction cos I don't know where to start!
[1] A particle of mass m moves in 3D space around a fixed attractive centre with the potential U(r)=-u/r. List all possible types of trajectories for this...
Hey, self-studying, I've just started into Marion's Classical Dynamics of Particles and Systems, and I'm having major issues with the problems; I don't even have any idea where to start. I was wondering if somebody would be willing to give some general advice and maybe go through a couple of...
Homework Statement
I need to find equations of motion of system on picture. It is easy when one finds Lagrangian so I am not asking you to calculate it, but I'm not sure if I correctly calculated the kinetic energy, so If anyone can verify, I would be greatfull.
The rod has mass m, length 2a...
Homework Statement
A comet is going in a parabolic orbit lying in the plane of Earth's Orbit. Regarding Earth's orbit as circular of radius "a," show that the points where the comet intersects Earth's orbit are given by:
cos(theta)= -1 + (2*p)/a where p is the perihelion distance of the...
Hello, people of the physics forums. I'm trying to get a grasp on physics, and I have come to my first real roadblock. I'm looking at Classical Mechanics, and more specifically, net displacement.
On http://farside.ph.utexas.edu/teaching/301/lectures/node20.html, I have attempted a set of...
Homework Statement
Show directly that the transformation; Q=log(1/q*sinp), P=q*cotp is canonical.Homework Equations
Since these equations have no time dependence, the equations are canonical if (with d denoting a partial derivative)
dQ_i/dq_j = dp_j/dP_i, and dQ_i/dp_j = -dq_j/dP_i
The...