Struct SecondVariation 

pub struct SecondVariation {
    pub functional: String,
    pub is_positive_definite: bool,
}

Second variation δ²F of a functional, used to classify critical points.

Fields

functional: String

Name of the functional.

is_positive_definite: bool

Whether the second variation operator is positive definite on the function space.

Implementations

impl SecondVariation

pub fn new(functional: impl Into<String>, is_positive_definite: bool) -> Self

Create a new SecondVariation (defaults to positive definite).

pub fn legendre_condition(&self) -> bool

Legendre necessary condition: L_{ẋẋ} ≥ 0 along the extremal. Returns true when is_positive_definite holds (sufficient form).

pub fn jacobi_condition(&self) -> bool

Jacobi sufficient condition: no conjugate points on the open interval. Returns true when the second variation is positive definite.

Trait Implementations

impl Clone for SecondVariation

fn clone(&self) -> SecondVariation

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for SecondVariation

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.