Tagged Questions

Newtonian mechanics covers the discussion of the movement of classical bodies under the influence of forces by making use of Newton’s three laws. For more general discussion of energy, momentum conservation etc., use classical-mechanics, for Newton’s description of gravity, use newtonian-gravity.

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Uniqueness of solution in newtonian mechanics

Recently I came across the problem of Norton's dome. I thought of two questions, for which I found no answer. Does there exist a newtonian initial value problem, where the total force on each body ...
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How can I approximate Jacobian Elliptic Functions in terms of basic integrable functions for the SO(3) rotation of a rigid body?

So, the rotation of a 3d body can be described with Euler's equations of motion giving the rotational velocity in components along the principal axes of inertia. As showed in f.ex. this paper, ...
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Barycenter correction for inner planets in solar system?

I want to run simulations of the solar system, and I've read in some papers that to speed up the simulations it is useful to use the barycenter correction of the inner planets (from Mercury to Mars), ...
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Gimbal Lock: why is it a problem?

I was watching this video http://www.youtube.com/watch?v=rrUCBOlJdt4 about the gimbal lock problem. I understood that during rotations it could happen that one DOF disappear. Looking at the middle ...
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Alternate Formulation of Kinetic Energy for Lagrangian

So I have a question regarding this system: It is supposed to be a simple model of an aircraft with the fuselage idealized as a concentrated mass $M_0$ and the wings modeled as rigid bars carrying ...
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How to efficiently cool down simulated gas by time-dependent potential?

I'm trying to simulate condensation of a highly diluted gas (a model gas, not any real one). For simplicity I restrict the simulation to 2 dimensions. To setup the simulation I take some interparticle ...
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Dark matter “hair” flowing through the earth

Gary Prézeau of NASA's JPL has done some calculations of how dark matter might be focussed by the Earth's gravitational field (publication preprint), and the results show some remarkable hairy ...
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From Newton to Kepler without infinitesimals

I've read some interesting calculus-free proofs of at least parts of the derivation of Kepler's Laws from Newton's gravitational force. One is of course Feyman's "Lost Lecture" (which was already ...
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Can one verify the Earth tide in his yard?

The ocean tide you can see on the coast. But the Earth tide beneath our feet is hardly perceivable. Is there any way to verify it in one's yard?
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Modelling an Inelastic Collision

I've attempted to model the inelastic collision between a moving mass and a large stationary object, e.g. dropping an ball on the floor, for analysing the approximate kinematics and heat dissipation ...
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how much force is necessary to move a 3368# airplane?

I have an airplane on tricycle gear (nosewheel and 2 main wheels under the wing). Sometimes I need to move it back and forth in the parking area. How much force must I apply to move it? The reason I'...
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How to find tension in the cantilever brakes?

In the left side example of cantilever brakes, how do I find the tension in strings DE and DC, in terms of T. According to me applying force balance equations, horizontal and vertical forces should be ...
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Aerosol size distribution

When the size distribution of particles in an aerosol is obtained, there is always a bimodal distribution. The small peak accounts for the particles that are in sub-nanometer size range and the larger ...
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Videos of changing the orientation of an astronaut in space

Kane, Headrick and Yatteau describe in their paper "Experimental investigation of an astronaut maneuvering scheme" possible maneuvers to change the orientation in space without external torque. Is ...
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Foucault pendulum, where did I go wrong?

I wanted to approximate the number $N$ of periodes needed, such that the foucault pendelum turns one time. Though my result is off by the factor 2 of the results I found. What I did: I assume the ...
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Physical motivation for one dimensional SHM superposition

Are there any real life, simple and mechanical system which motivate the study of Simple Harmonic Motion (SHM) superposition in one dimension? I am preparing a lecture about it but I have not seen any ...
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What happens to Newton's Third Law during the reflection of a pulse from a free end?

Well, it is known that a pulse gets inverted when it gets reflected from a fixed support while the polarity of the pulse remains same when the incident pulse gets reflected from a free end. However, ...
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Stability of plants and buildings: the role of the xylem

Dicotyledon plants show a stem structure with many xylem tubes, hollow but with lignified (woody) walls. These are arranged as in the figure below, in a circle. Their roots, on the other hand, have ...
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To prove uniqueness of the rotation tensor associated with rotation of a rigid body

Suppose there are $N$ particles embedded in a rigid body which undergoes some random rotation such that: $$\overline{\overline {R}}_{ij} \otimes \vec{a}_{ij} = \vec{b}_{ij}$$ where, $i$ and $j$...
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Centrifugal Force vs Motion (inertia)

Could centrifugal force be appropriately described as motion (inertia)--rather than an (imaginary) force? Could such a change of perspective eliminate much of the common confusion?
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Newton's mechanics. Axioms, postulates, etc

I am trying to write all the assumptions or postulates to set up Newton's mechanics: 1.- The space is infinite, continuous, homogeneous, isotropic and 3-dimensional. By this way, we assume that the ...
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I'm doing some revision using a study guide before the semester starts up again, and have gotten stuck on part of a question. The question I’m having trouble with is as follows: A rock of mass $m = 1.... 0answers 73 views Precession of angular momentum vector I'm studying Classical Mechanics on Goldstein's book, so I'm using his terminology and notation. First I'll explain where the question comes from: consider a heavy symmetrical top and consider the ... 0answers 140 views Lagrange: when a potential force, when a generalized force? Consider the following case of a drum unrolling a mass that is on a massless string wrapped around the drum: According to my professor, here we must consider the mass$m$being in a gravitational ... 0answers 25 views Initial conditions for a massive objects to follow a path Suppose I have a path, such as the one traced out by$r^2 = \cos(2\theta)$, and$n$objects with mass$m$at equidistant points on this path. What velocities should each object initially have in order ... 0answers 102 views Why do Lagrange multipliers work in mechanics? I understand that it is not always simple to find generalized coordinates that satisfy the constraint equations, so we try to find an alternative (more mechanical) method that yields curves that ... 0answers 71 views Trouble with geometric proof of gravitational force inside a sphere In Newton's superb theorem: An elementary geometric proof (Argument on Page 4, accompanying diagram on Page 11), the author attempts to prove Proposition 70 in Newton's Principia (gravitational force =... 0answers 47 views The underlying chemical interactions behind torque I did some searching around, and didn't find any previous topics that address torque in this specific way -- here goes: Say I just have a plain ol' piece of wood -- relatively long in one axis, so it ... 0answers 196 views 3D Simulation Software I need a software capable of simulating the physics of a car going off a ramp. This is a stunt that I will be attempting and looks like the following: A car, going off a curved ramp, doing a barrel ... 0answers 24 views Creating a structural dynamic model using only modal test data Short version: Suppose I excite a vibrational response in some structure and measure its mode shapes and natural frequencies. Is it possible to create a structural dynamic model of the structure ... 0answers 35 views What kind of forces would follow only the second part of shell theorem? General expression of a force which would cancel out inside a uniform hollow shell. What about any closed surface? 0answers 53 views What is the effect of vibrations on an object's properties? What do vibrations do to an object's properties? By making an object vibrate at a high frequency (compared to its static state) would vibrations: Increase or reduce its moment of inertia? Increase ... 0answers 93 views Why did Feynman tell “we cannot locate earth's angular position, but we can tell that it is changing”? I was reading "Symmetry in physics" by Feynman, where he wrote: If we perform sufficiently delicate experiments, we can tell that the earth is rotating, but not that it had rotated. In other words,... 0answers 113 views Motion of a charged particle in a “solid” charged sphere (accounting for radiation) Consider a particle (point charge) with charge$q$and mass$m$that crosses into a uniformly charged sphere (with charge$Q$and radius$R$). The trajectory of the particle is a diameter of the ... 0answers 71 views Can a projectile moving at supersonic velocities leave a silhouette in whatever it hits? I was recently reading this, and Floris's answer confirmed my knowledge that the information of an collision travels at the speed of sound. While I was thinking about that, my mind wandered and I ... 0answers 224 views Maximum friction force for a wheel to be able to roll The wheel with mass$M$and radius$R$below is free in space (it is not on the ground). A torque$\tau$is applied to it through an engine. A horizontal force$F = \frac{\tau}{R}$is also applied to ... 0answers 254 views How to calculate launch angle for tangentially launched satellites? What is the value of theta for a satellite not falling back to the Earth if it is launched from the direction tangent to the surface of the Earth? I have found the escape velocity which is 11.18km/s, ... 0answers 622 views Sum of energy in a free rotation with Algodoo software I try to understand why Algodoo software (freeware) give an efficiency greater than unity. I tested several scenes and at each time I can look the software give energy, I don't say it's all the time ... 0answers 148 views Only gravitation and Newton's$2^{\mathrm{nd}}$law needed to derive Kepler's laws? It is known that Kepler's laws of planetary motion can be derived from Newton's laws of motion and his law of universal gravitation. However, are all of Newton's laws of motion necessary? According ... 0answers 109 views what forces are present when slicing an object. I found here:What happens when we cut objects? that it is due to fracture wood splits open when using a wedge. Does it only apply when the wedge is already in the wood? How about the moment before a ... 0answers 105 views Can I use the reduced mass principle in a spring-damper system? http://hyperphysics.phy-astr.gsu.edu/hbase/orbv.html#rm I want to know, if I can use the reduced mass principle to solve a two object spring-damper system. In the books and webpages that I have ... 0answers 161 views Jacobian matrix of Galilean transformation If we want to transform to another inertial frame of reference using Galilean transformation in 4-dimensional space-time, what is the Jacobian matrix of Galilean transformation? 0answers 118 views Seeking help simplifying this EOM equation I am working on solving the equation of motion for a particular system. It has been a long time since I've worked with matrix equations and need help in simplifying the following:$\frac{d}{dt}$$(I_G\... 0answers 214 views N-body forces in classical mechanics For a system of two interacting particles 1, 2 we get from the conservation of momentum$$ \dot{\bf{p_1}} + \dot{\bf{p_2}} = 0$$... 0answers 303 views Air resistance of a general shape object I'm trying to code a simple physics simulator in C++ but I'm stuck on the air resistance issue. Surfing the Internet I only find a drag coefficient for very basical area shapes when the air is ... 0answers 426 views Mechanics of Materials (pressure and temperature) A solid right cylinder of rock core is surrounded by four rods made of mild steel (all-thread rods). The rods are placed equidistantly around the core in a square formation. The tops and bottoms of ... 0answers 476 views Why did increasing the Ackermann geometry in my race car make it faster in corners? Ackermann geometry is used to account for the different radius arcs that the front tires follow when the steering wheel is turned from center. It's often expressed as a percentage: e.g. 25% Ackermann, ... 0answers 212 views Semiflexible discrete polymer chain Suppose we have a 2D polymer model described by a set of 2D vectors {\mathbf{t}_i} (i=1,2,\dots N) of length a. The energy of the polymer is given by:$$ \mathcal{H}~=~-k\sum^N_{i=1}\mathbf{t}...
For a simulation for testing on automatic cruise control, I came across the equation: $$v_{n+1} = (1 - k_1 / m) v_n + (1 - k_b) \begin{pmatrix} T_n \\ θ_n \\ \end{pmatrix}$$ where: $T$ = ...