Mechanical Vibrations 17 - Equilibrium Configurations

  Рет қаралды 5,857

Jurnan Schilder

Jurnan Schilder

Күн бұрын

Пікірлер
@Bertnijkamp1995
@Bertnijkamp1995 4 жыл бұрын
If you would just look at the equation of motion/equilibrium (so without looking at the physical situation), are you able to determine whether an equilibrium configuration is stable or unstable?
@JurnanSchilder
@JurnanSchilder 4 жыл бұрын
Yes you are! For this you need to have the nonlinear EoM. Then you determine the equilibria. Then you can linearize the EoM around an equilibrium and compute the eigenvalues (think: natural frequencies). If at least one of the eigenvalues have a positive real part, the general solution will contain an exponential function with a positive exponent. This will blow up in time and thus represents unstable behaviour. If all eigenvalues are negative (or complex with a negative real part) we have a stable solution. Eigenvalues that are purely imaginary represent undamped vibrations. You could do this linearization and solve the EVP for every equilibrium configuration to determine which of them are stable and which of them are not.
@abhishekpg9615
@abhishekpg9615 2 жыл бұрын
Should we include the force mg in equation of motion because if we consider the static deflection then mg and static deflection would cancel out right?
Mechanical Vibrations 18 - Linearization
14:20
Jurnan Schilder
Рет қаралды 7 М.
Mechanical Vibrations 10 - Newton-Euler 1 - Rolling Disk
13:11
Jurnan Schilder
Рет қаралды 12 М.
БАБУШКА ШАРИТ #shorts
0:16
Паша Осадчий
Рет қаралды 4,1 МЛН
Непосредственно Каха: сумка
0:53
К-Media
Рет қаралды 12 МЛН
Жездуха 41-серия
36:26
Million Show
Рет қаралды 5 МЛН
Understanding Vibration and Resonance
19:42
The Efficient Engineer
Рет қаралды 1,3 МЛН
Mechanical Vibrations 8 - Newton 2 - Double Mass-spring-damper system
12:00
UA - ME 431: Lagrange's Equations, Example
25:26
Dane Quinn
Рет қаралды 8 М.
Mechanical Vibrations 15 - Lagrange 3 - Nonconservative systems
14:03
Jurnan Schilder
Рет қаралды 13 М.
Visualization of tensors  - part 1
11:41
udiprod
Рет қаралды 624 М.
The Dome Paradox: A Loophole in Newton's Laws
22:59
Up and Atom
Рет қаралды 1,2 МЛН
Chaos Theory: the language of (in)stability
12:37
Gonkee
Рет қаралды 578 М.
Pendulums, Resonance & Resonant Frequency in Physics - [2-2-4]
50:53
Math and Science
Рет қаралды 5 М.
What's a Tensor?
12:21
Dan Fleisch
Рет қаралды 3,7 МЛН
Mechanical Vibrations 49 - Strings 6 - Forced Vibrations
16:05
Jurnan Schilder
Рет қаралды 2,8 М.
БАБУШКА ШАРИТ #shorts
0:16
Паша Осадчий
Рет қаралды 4,1 МЛН