5. Лексика и фразеология

2.5.1. Since these early references…

Since. – См. 1.5.1.

2.5.2. The literature has become too vast…

Too. Перевод слова «тоже»

В начале и середине предложения too – «слишком» (too big). В конце предложения too – «тоже» (I like it, too). Если в предложении есть отрицание, вместо too употребляется either (I don’t like it either). Слово «тоже» может переводиться also (тоже, также, к тому же; ставится в середине предложения): I also like it.

Задание 1. Переведите: 1) It is too good to be true. 2) I can do it, too. 3) He can’t do it either. 4) We also can do it.

Задание 2. Переведите: 1) Он тоже студент. 2) Он также и студент. 3) Он также любит математику. 4) Он тоже любит математику. 5) Он тоже не любит математику.

2.5.3. Examples like the double spherical pendulum…

Like. Основные значения

1. «Любить»; в обратных конструкциях – «нравиться» (I like him – Он мне нравится).

2. «Как», «наподобие» (см. 2.3.18); like that – так.

3. «Подобный»: like terms – подобные члены.

Задание. Переведите: 1) Don’t talk like that. 2) She sings like a bird. 3) Do as you like. 4) These are like terms.

2.5.4. The history of stability theory…

Перевод слова «история»

History – 1) история (прошлое); 2) история (наука).

Story – история (рассказ).

Задание. Переведите: интересная история; история кино; много историй; современная история; изучать историю.

2.5.5. Small disturbances do not grow large…

Grow

Grow – 1) расти, 2) выращивать, 3) становиться (ср. turn – 1.5.4).

Задание. Переведите: to grow in the forest; to grow dark; to grow roses; to grow large; to grow not older but younger; to grow quickly.

2.5.6. There are various meanings; stability means that…

Mean и его производные

Mean (глаг.) – 1) означать; 2) подразумевать; 3) намереваться.

Mean (сущ.) – середина.

Mean (прил.) – 1) средний; 2) посредственный; 3) низкий, подлый; 4) скупой.

Means (сущ.) – 1) (часто употребляется как ед.ч.) средство, способ; 2) средства, состояние, богатство.

By means of – посредством; by all means – любым способом, любой ценой; by no means – никоим образом; нисколько.

Meaning (сущ.) – значение.

Задание. Переведите: 1) What does it mean? 2) What do you mean? 3) I’m sorry, I didn’t mean. 4) It is the golden mean. 5) What is the meaning of this word? 6) He wanted to get it by all means. 7) Draw the mean line. 8) He is a mean person. 9) Is it true? – By no means! 10) We can’t live without means of communication. 11) He is a man of means. 12) It is a mean work. 13) We think by means of the brain.

2.5.7. As time passes

As. Основные значения

As – 1) как (см. 2.3.18); 2) в качестве (см. 1.3.4.5.1); 3) когда; 4) так как; 5) по мере того как.

As for – что касается.

As if (as though) – как будто (дословно: как если бы).

As… as – так(ой) же… как…

No so (as)… as… – не такой, как… (см. 2.3.18).

As well as – так же, как.

As well – так же.

Задание. Переведите: 1) He works as a doctor. 2) As it was too late, I didn’t do it. 3) As for me, I don’t like coffee. 4) He is as busy as a bee. 5) He behaved as if he were mad. 5) Do as I tell you. 6) As I was walking in the park, I saw a nice girl. 7) It doesn’t change as time passes. 8) He could do it as well. 9) He could do it as well as I could.

2.5.8. The nonlinear stability method discussed below

Discuss

Discuss – обсуждать, дискутировать; 2) рассматривать, исследовать.

Задание. Переведите: 1) They read stories and then discussed them. 2) In this part of the article the history of the problem is discussed.

2.5.9. Instances of the same method

Перевод слов «такой», «такой же»

Such – такой.

После such ставится артикль a/an, где можно (т.е. в ед.ч. перед исчисляемыми существительными).

The same – такой же, тот же (всегда с артиклем; не путать с some).

As… as… – так(ой) же…, как… (см. 2.3.18).

Задание. Переведите: 1) Это приводит к таким же результатам. 2) Моя жизнь никогда не будет (will never be) такой же. 3) Такое решение (decision) было опасно (dangerous). 4) Она такая же красивая, как моя сестра. 5) Я не люблю таких слов.

Text 3. Dynamics and Stability

Stability is a dynamical concept. To explain it, we shall use some fundamental notions from the theory of dynamical systems (see, for example, Hirsch and Smale [1974] and Guckenheimer and Holmes [1983]). The laws of dynamics are usually presented as equations of motion, which we write in the abstract form of a dynamical system:

= X(u). (1.7.1)

Here, u is a variable describing the state of the system under study, X is a system-specific function of u, and = du/dt, where t is time. The set of all allowed u's forms the state, or phase space P. We usually view X as a vector field on P. For a classical mechanical system, u is often a 2n-tuple (q¹, ... , qⁿ, p₁, ... , p_n) of positions and momenta, and for fluids, u is a velocity field in physical space.

As time evolves, the state of the system changes; the state follows a curve u(t) in P. The trajectory u(t) is assumed to be uniquely determined if its initial condition u₀ = u(0) is specified. An equilibrium state is a state u_e such that X(u_e) = 0. The unique trajectory starting at u_e is u_e itself; that is, u_e does not move in time.

The language of dynamics has been an extraordinarily useful tool in the physical and biological sciences, especially during the last few decades. The study of systems that develop spontaneous oscillations through a mecha­nism called the Poincaré–Andronov–Hopf bifurcation is an example of such a tool (see Marsden and McCracken [1976], Carr [1981], and Chow and Hale [1982], for example). More recently, the concept of "chaotic dynamics" has sparked a resurgence of interest in dynamical systems. This occurs when dynamical systems possess trajectories that are so complex that they be­have as if they were, in some sense, random. Some believe that the theory of turbulence will use such notions in its future development. We are not concerned with chaos directly, although it plays a role in some of what follows. In particular, we remark that in the definition of stability below, stability does not preclude chaos. In other words, the trajectories near a stable point can still be temporally very complex; stability just prevents them from moving very far from equilibrium.