Francesco Fassò
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Francesco Fassò has a total of 32 co-authors. Here are the top co-authors by number of shared publications:
- Nicola Sansonetto
Università di Verona
8 shared publications - Andrea Giacobbe
Università di Padova Dipartimento di Matematica Via Trieste 63 35131 Padova Italy
5 shared publications - Luis C. Garcia-Naranjo
Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova, Padova, Italy
5 shared publications - Nicola Sansonetto
Dipartimento di Matematica Università di Padova Via Trieste 63 35121 Padova Italy
4 shared publications - Antonio Ponno
Università degli Studi di Padova
2 shared publications - Daniele Fontanari
Université du Littoral Côte d’Opale
2 shared publications
Latest Publications
- Open Access
- 1 January 2025
- Published by National Library of Serbia in Theoretical and Applied Mechanics
- Vol. 52 (1) , 17-37
Point spectra and normal modes of the Rayleigh loaded string with damping
We describe the point spectra of some dissipative version of the celebrated ?Rayleigh loaded string?, an elastic string of finite length carrying a number n ? 1 of equally spaced, equal point masses, which is a basic model that exhibits a band structure and appears in many applied areas. We consider the case in which the dissipation is due to a viscous damping due to the interaction string-environment, a standard model for internal visco-elastic dissipation (the Kelvin-Voigt model), and their combined presence. We show that the point spectrum of each of these damped versions of the Rayleigh loaded string is a continuous deformation of the point spectrum of the unloaded elastic strings with that damping and that presents a band structure similar to that of the undamped case. We also provide explicit analytical expressions for the eigenfunctions, for any value of n.
- 1 January 2025
- Published by National Library of Serbia in Theoretical and Applied Mechanics
- Vol. 52 (1) , 17-37
Open AccessPoint spectra and normal modes of the Rayleigh loaded string with damping
We describe the point spectra of some dissipative version of the celebrated ?Rayleigh loaded string?, an elastic string of finite length carrying a number n ? 1 of equally spaced, equal point masses, which is a basic model that exhibits a band structure and appears in many applied areas. We consider the case in which the dissipation is due to a viscous damping due to the interaction string-environment, a standard model for internal visco-elastic dissipation (the Kelvin-Voigt model), and their combined presence. We show that the point spectrum of each of these damped versions of the Rayleigh loaded string is a continuous deformation of the point spectrum of the unloaded elastic strings with that damping and that presents a band structure similar to that of the undamped case. We also provide explicit analytical expressions for the eigenfunctions, for any value of n.
- Open Access
Symplectization of certain Hamiltonian systems in fibered almost-symplectic manifolds
There is an important difference between Hamiltonian-like vector fields in an almost-symplectic manifold $(M,σ)$, compared to the standard case of a symplectic manifold: in the almost-symplectic case, a vector field such that the contraction iXσ is closed need not be a symmetry of $σ$. We thus call partially-Hamiltonian those vector fields which have the former property and fully-Hamiltonian those which have both properties. We consider 2n-dimensional almost symplectic manifolds with a fibration $π: M \longrightarrow B$ by Lagrangian tori. Trivially, all vertical partially-Hamiltonian vector fields are fully-Hamiltonian. We investigate the existence and the properties of non-vertical fully-Hamiltonian vector fields. We show that this class is non-empty, but under certain genericity conditions that involve the Fourier spectrum of their Hamiltonian, these vector fields reduce, under a (possibly only semi-globally defined, if $n \ge 4$) torus action, to families of standard symplectic-Hamiltonian vector fields.Open AccessSymplectization of certain Hamiltonian systems in fibered almost-symplectic manifolds
There is an important difference between Hamiltonian-like vector fields in an almost-symplectic manifold $(M,σ)$, compared to the standard case of a symplectic manifold: in the almost-symplectic case, a vector field such that the contraction iXσ is closed need not be a symmetry of $σ$. We thus call partially-Hamiltonian those vector fields which have the former property and fully-Hamiltonian those which have both properties. We consider 2n-dimensional almost symplectic manifolds with a fibration $π: M \longrightarrow B$ by Lagrangian tori. Trivially, all vertical partially-Hamiltonian vector fields are fully-Hamiltonian. We investigate the existence and the properties of non-vertical fully-Hamiltonian vector fields. We show that this class is non-empty, but under certain genericity conditions that involve the Fourier spectrum of their Hamiltonian, these vector fields reduce, under a (possibly only semi-globally defined, if $n \ge 4$) torus action, to families of standard symplectic-Hamiltonian vector fields. - Open Access
Point spectra and normal modes of the Rayleigh loaded string with damping
We describe the point spectra of some dissipative version of the celebrated "Rayleigh loaded string", an elastic string of finite length carrying a number n ≥ 1 of equally spaced, equal point masses, which is a basic model that exhibits a band structure and appears in many applied areas. We consider the case in which the dissipation is due to a viscous damping due to the interaction string-environment, a standard model for internal visco-elastic dissipation (the Kelvin-Voigt model), and the combined presence of them. We show that the point spectrum of each of these damped versions of the Rayleigh loaded string is a continuous deformation of the point spectrum of the unloaded elastic strings with that damping and that presents a band structure similar to that of the undamped case. We also provide explicit analytical expressions for the eigenfunctions, for any value of n.
Open AccessPoint spectra and normal modes of the Rayleigh loaded string with damping
We describe the point spectra of some dissipative version of the celebrated "Rayleigh loaded string", an elastic string of finite length carrying a number n ≥ 1 of equally spaced, equal point masses, which is a basic model that exhibits a band structure and appears in many applied areas. We consider the case in which the dissipation is due to a viscous damping due to the interaction string-environment, a standard model for internal visco-elastic dissipation (the Kelvin-Voigt model), and the combined presence of them. We show that the point spectrum of each of these damped versions of the Rayleigh loaded string is a continuous deformation of the point spectrum of the unloaded elastic strings with that damping and that presents a band structure similar to that of the undamped case. We also provide explicit analytical expressions for the eigenfunctions, for any value of n.
- 17 December 2022
- Published by Springer Nature
- p. 307-337
Perturbation of Superintegrable Hamiltonian Systems
- 17 December 2022
- Published by Springer Nature
- p. 307-337
Perturbation of Superintegrable Hamiltonian Systems
- 27 September 2022
- Published by Springer Nature
- p. 1-31
Perturbations of Superintegrable Hamiltonian Systems
- 27 September 2022
- Published by Springer Nature
- p. 1-31
Perturbations of Superintegrable Hamiltonian Systems
- Open Access
- 14 September 2022
- Published by EDP Sciences in ESAIM: Mathematical Modelling and Numerical Analysis
- Vol. 56 (6) , 1939-1954
Computing the cut locus of a Riemannian manifoldviaoptimal transport
In this paper, we give a new characterization of the cut locus of a point on a compact Riemannian manifold as the zero set of the optimal transport density solution of the Monge–Kantorovich equations, a PDE formulation of the optimal transport problem with cost equal to the geodesic distance. Combining this result with an optimal transport numerical solver, based on the so-called dynamical Monge–Kantorovich approach, we propose a novel framework for the numerical approximation of the cut locus of a point in a manifold. We show the applicability of the proposed method on a few examples settled on 2d-surfaces embedded in ℝ3, and discuss advantages and limitations.
- 14 September 2022
- Published by EDP Sciences in ESAIM: Mathematical Modelling and Numerical Analysis
- Vol. 56 (6) , 1939-1954
Open AccessComputing the cut locus of a Riemannian manifoldviaoptimal transport
In this paper, we give a new characterization of the cut locus of a point on a compact Riemannian manifold as the zero set of the optimal transport density solution of the Monge–Kantorovich equations, a PDE formulation of the optimal transport problem with cost equal to the geodesic distance. Combining this result with an optimal transport numerical solver, based on the so-called dynamical Monge–Kantorovich approach, we propose a novel framework for the numerical approximation of the cut locus of a point in a manifold. We show the applicability of the proposed method on a few examples settled on 2d-surfaces embedded in ℝ3, and discuss advantages and limitations.
- Open Access
- 11 September 2022
- Published by Springer Nature in Journal of Nonlinear Science
- Vol. 32 (6) , 1-45
On the Dynamics of a Heavy Symmetric Ball that Rolls Without Sliding on a Uniformly Rotating Surface of Revolution
We study the class of nonholonomic mechanical systems formed by a heavy symmetric ball that rolls without sliding on a surface of revolution, which is either at rest or rotates about its (vertical) figure axis with uniform angular velocity $$\Omega $$ . The first studies of these systems go back over a century, but a comprehensive understanding of their dynamics is still missing. The system has an $$\mathrm {SO(3)}\times \mathrm {SO(2)}$$ symmetry and reduces to four dimensions. We extend in various directions, particularly from the case $$\Omega =0$$ to the case $$\Omega \not =0$$ , a number of previous results and give new results. In particular, we prove that the reduced system is Hamiltonizable even if $$\Omega \not =0$$ and, exploiting the recently introduced “moving energy,” we give sufficient conditions on the profile of the surface that ensure the periodicity of the reduced dynamics and hence the quasiperiodicity of the unreduced dynamics on tori of dimension up to three. Furthermore, we determine all the equilibria of the reduced system, which are classified in three distinct families, and determine their stability properties. In addition to this, we give a new form of the equations of motion of nonholonomic systems in quasi-velocities which, at variance from the well-known Hamel equations, use any set of quasi-velocities and explicitly contain the reaction forces.- 11 September 2022
- Published by Springer Nature in Journal of Nonlinear Science
- Vol. 32 (6) , 1-45
Open AccessOn the Dynamics of a Heavy Symmetric Ball that Rolls Without Sliding on a Uniformly Rotating Surface of Revolution
We study the class of nonholonomic mechanical systems formed by a heavy symmetric ball that rolls without sliding on a surface of revolution, which is either at rest or rotates about its (vertical) figure axis with uniform angular velocity $$\Omega $$ . The first studies of these systems go back over a century, but a comprehensive understanding of their dynamics is still missing. The system has an $$\mathrm {SO(3)}\times \mathrm {SO(2)}$$ symmetry and reduces to four dimensions. We extend in various directions, particularly from the case $$\Omega =0$$ to the case $$\Omega \not =0$$ , a number of previous results and give new results. In particular, we prove that the reduced system is Hamiltonizable even if $$\Omega \not =0$$ and, exploiting the recently introduced “moving energy,” we give sufficient conditions on the profile of the surface that ensure the periodicity of the reduced dynamics and hence the quasiperiodicity of the unreduced dynamics on tori of dimension up to three. Furthermore, we determine all the equilibria of the reduced system, which are classified in three distinct families, and determine their stability properties. In addition to this, we give a new form of the equations of motion of nonholonomic systems in quasi-velocities which, at variance from the well-known Hamel equations, use any set of quasi-velocities and explicitly contain the reaction forces. - 1 July 2022
- Published by Pleiades Publishing Ltd in Regular and Chaotic Dynamics
- Vol. 27 (4) , 409-423
On Some Aspects of the Dynamics of a Ball in a Rotating Surface of Revolution and of the Kasamawashi Art
We study some aspects of the dynamics of the nonholonomic system formed by a heavy homogeneous ball constrained to roll without sliding on a steadily rotating surface of revolution. First, in the case in which the figure axis of the surface is vertical (and hence the system is \(\textrm{SO(3)}\times\textrm{SO(2)}\)-symmetric) and the surface has a (nondegenerate) maximum at its vertex, we show the existence of motions asymptotic to the vertex and rule out the possibility of blowup. This is done by passing to the 5-dimensional SO(3)-reduced system. The SO(3)-symmetry persists when the figure axis of the surface is inclined with respect to the vertical — and the system can be viewed as a simple model for the Japanese kasamawashi (turning umbrella) performance art — and in that case we study the (stability of the) equilibria of the 5-dimensional reduced system.- 1 July 2022
- Published by Pleiades Publishing Ltd in Regular and Chaotic Dynamics
- Vol. 27 (4) , 409-423
On Some Aspects of the Dynamics of a Ball in a Rotating Surface of Revolution and of the Kasamawashi Art
We study some aspects of the dynamics of the nonholonomic system formed by a heavy homogeneous ball constrained to roll without sliding on a steadily rotating surface of revolution. First, in the case in which the figure axis of the surface is vertical (and hence the system is \(\textrm{SO(3)}\times\textrm{SO(2)}\)-symmetric) and the surface has a (nondegenerate) maximum at its vertex, we show the existence of motions asymptotic to the vertex and rule out the possibility of blowup. This is done by passing to the 5-dimensional SO(3)-reduced system. The SO(3)-symmetry persists when the figure axis of the surface is inclined with respect to the vertical — and the system can be viewed as a simple model for the Japanese kasamawashi (turning umbrella) performance art — and in that case we study the (stability of the) equilibria of the 5-dimensional reduced system.- Open Access
Computing the Cut Locus of a Riemannian Manifold via Optimal Transport
In this paper, we give a new characterization of the cut locus of a point on a compact Riemannian manifold as the zero set of the optimal transport density solution of the Monge-Kantorovich equations, a PDE formulation of the optimal transport problem with cost equal to the geodesic distance. Combining this result with an optimal transport numerical solver based on the so-called dynamical Monge-Kantorovich approach, we propose a novel framework for the numerical approximation of the cut locus of a point in a manifold. We show the applicability of the proposed method on a few examples settled on 2d-surfaces embedded in $R^{3}$ and discuss advantages and limitations.Open AccessComputing the Cut Locus of a Riemannian Manifold via Optimal Transport
In this paper, we give a new characterization of the cut locus of a point on a compact Riemannian manifold as the zero set of the optimal transport density solution of the Monge-Kantorovich equations, a PDE formulation of the optimal transport problem with cost equal to the geodesic distance. Combining this result with an optimal transport numerical solver based on the so-called dynamical Monge-Kantorovich approach, we propose a novel framework for the numerical approximation of the cut locus of a point in a manifold. We show the applicability of the proposed method on a few examples settled on 2d-surfaces embedded in $R^{3}$ and discuss advantages and limitations.