Viena uzdevuma divas sejas: apgriezto kvadrātu likums astperei un

lielas amplitūdas svārsts

Slava Kaščejevs

LU DF un FMF

LU 69. zinātniskā konference 2011. gada 2. februārī

ESF projekts Nr. 2009/0216/1DP/1.1.1.2.0/09/APIA/VIAA/044 „Datorzinātnes pielietojumi un tās saiknes ar kvantu fiziku”

Antonio Šiber Hrvoje Buljan

Energy functional (Kircchoff rod)

Constraint of fixed width:

Tangential angle parametrization:

Curvature:

The main idea

W – equilibrium (potential) energy W – dynamical action (= kinetic minus potential energy)

s – natural length s – time

θ – tangent angle θ – pendulum angle

ω02 – elastic force (Lagrange multiplier) ω0 – linear frequency

Critical profile: zero initial curvatre = 90o initial deviation for pendulum

Critical profile shape (indepdent of units):

universal

Theory versus experiment

Stability and tension

Paldies!