Mechanical systems Definition and 24 Threads

How to handle a variable mass system with Lagrangian mechanics? As far as I understand Newtonian mechanics fails, because the object is not constant anymore, it is updated every moment to a new object with different physical properties. I don't immediately see how Lagrangian mechanics can do better.

I'm studying theoretical mechanics and I kind of find the notion of a "mechanical system" very slippery, especially when it comes to constraints. Take an example : I know that when a system consists of N particles and p constraints, it has 3N-p degrees of freedom; this is the definition. Then I...

Hello I have used and enjoyed the textbook: "Theory of Vibrations with Applications," by William Thomson However, many of the examples there are more civil engineering than mechanical. There are many good examples of "buildings" under vibrations (good examples, but civil, nonetheless) The few...

Greetings, I'd like to simulate a complex mechanical automaton with lots of gears, cams, levers and springs. Most of the parts are going to be 3D printed except for some metal springs, rods and bearings. I want to make sure everything fits together and works as expected. Here is just a small...

Homework Statement Given an isolated system of 2 particles in space, we can express the motion of both particles as follows: $$m_1\ddot{\vec{x_1}}=-\frac\partial{\partial \vec{x_{1}}} V(\vec{x_1},\vec{x_2})\\ m_2\ddot{\vec{x_2}}=-\frac\partial{\partial \vec{x_2}} V(\vec{x_1},\vec{x_2}),$$ where...

Homework Statement Find equations of motion for mechanical system given by picture, where m = 1kg, k1 = 10, k2 = 25, b = 3 and natural lengths of springs are a1 = 1m, a2 = 2m. The whole system is in a gravitational field g = 9.81m/s^2 Homework EquationsThe Attempt at a Solution I came up with...

I would like to discuss here some points from the article Martin Swaczyna Several examples of nonholonomic mechanical systems Communications in Mathematics, Vol. 19 (2011), No. 1, 27--56 This article is available at https://eudml.org/doc/196963 Let us open page 37: This is a classical problem...

Hello all, I require your expertise on building an approach or a framework to identify and measure the jerk or vibration in a mechanical system with a slider. What I have is a slider (S) with a vertical link (L1) attached to it and another horizontal link (L2) attached at the tip of the link...

Hi I was given the following problem in my coursework: Homework Statement "A spring is initially compressed by 50mm when a steel ball of mass 2kg is released from just being in contact with the uncompressed spring. Determine the spring stiffness (k) of the spring." Homework Equations F = mg...

Hi All, So glad to have come across this amazing site and resource. I am a mature student completing an engineering degree with the Open University and I am after some guidance and help with creating a way to plot forces from a moving mechanical system. The images on the attached drawing are...

I'm looking for a textbook on designing mechanical systems with multiple machine components. I'd like to study both rigid and non rigid dynamic systems. I'm open to studying systems composed of any mechanical component. In particular, I'd like to learn 1. draw accurate Free Body(FBD) and...

CONCEPTUAL QUESTIONS: -Does the Homogenous Solution represent the Transient Response? Let me specify. For a N-DOF spring, mass, and damper mechanical system: -Does the Homogenous Solution represent the Transient Response for given mechanical system? MY ANSWER: Yes. ASSUMPTIONS: -only...

I'm looking for a book that has problems and explanations (not necessarily background theory) about mechanical systems. Consider the picture below for reference. The idea is I want to get a hold of energy and impulse methods for solving problems like this, eventually the book would have a...

There are many formal definitions of an ergodic mechanical system. 1) A system whose time average equals the ensemble (space) average. 2) A system that visits every point in its phase space. Etc. What are some actual, real examples of an ergodic mechanical system? Also, since a chaotic...

I suppose some of you know the game called "Bridge Builder" (or Pontifex, or clones). I need some help determining how many FLOPS are required during the simulation and how do they scale with the bridge size (number of elements). Some of these bridges contain hundreds of elements and tens of...

Homework Statement Oscillation in mechanical structures can often be described by the function: y(t)=(e^(-t/τ))*sin(ωt+θ) Where t is time , ω is oscillation frequency in radians per unit time. The oscillations have a period of 2*π/ω and their amplitudes decay in time at a rate...

Homework Statement B, K, M Homework Equations 1. xs(t) -----spring ----mass-----damper-----fixed, derive DE for x of mass given :2. F - > M -----spring-------damper ---- fixed in series, derive the DE for velocity of spring The Attempt at a Solution 1. ma = -k(x-xs) -...

Homework Statement So I have this question given to me, basically there is a aero simulator which makes the ground shake so the data logger gets false readings, now to solve this problem a vibration absorption system has been added. Please see the attached System A.png file for the complete...

I want to start modeling mechanical systems, something say on the order of a motor, input torque only needed, driving a crankshaft that drives a piston. I'm looking to examine the forces generated in the crank, connecting rod and piston. I was wondering what open source Linux packages are...

Oscillating mechanical systems. find maximum velocity and acceleration !? A mass of 0.3 kg is suspended from a spring of stiffness 200 N m–1. If the mass is displaced by 10 mm from its equilibrium position and released, for the resulting vibration A) Calculate maximum velocity B) Calculate...

Hello, I know that blackbody radiation was one phenomenon whose study contributed to the conceptual development of QM early on. My first question is, what other such systems were considered? I want to know this because I'm closely following the actual order of development of QM concepts, the...

Mechanical systems - Please help me with this question! :( Person_Number M (kg) D (m) R (m/s2) <431383> 2700 60 1.4 Mechanical Systems Engineering Assignment 1 An unloaded lorry of mass M kg accelerates from rest and reaches a velocity of 30mph in 10 seconds. It...

1. If anyone is able to cast an eye over my work and comment would be appreciated. Q. A mass attached to the lower end of a vertical spring causes the spring to extend by 25mm to its equilibrium position. The mass is then displaced a further 20mm and released. A trace vibration and time...

Hi... I've been seeing a lot of job postings looking for engineers for designing and engineering mechanical building systems such as: HVAC systems, refrigeration systems, fire protection systems, plumbing and piping systems for some new commercial building developments. I am about to complete my...